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... These particular states of a quantum system were first mentioned by Einstein, Podolsky and Rosen in their famous EPR article of 1935 [13] and in quantum information theory (QIT) they can be considered as a fundamental physical resource (see, e.g., [25]). Entangled states turn out to be essential in many areas of QIT such as quantum error correcting codes [17], quantum key distribution [14] or quantum secret sharing [9]. Spectacular applications such as superdense coding [5] or quantum teleportation [15,39,42] are based on the use of classical entangled states. ...

... Using this convention and the isomorphism , Identity (14) becomes in GL n (F 2 ): ...

... Using Identity(14) in a CNOT 4 circuit ...

We study quantum circuits composed of a sequence of CNOT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\texttt {CNOT}$$\end{document} gates between distant qubits of a n-qubit system. We present some results concerning two important topics related to these circuits: circuit optimization and emergence of entanglement. Regarding the optimization problem, we first describe the group structure underlying quantum circuits generated by CNOT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\texttt {CNOT}$$\end{document} gates (group isomorphism, group presentation), then we apply these mathematical results to the description of heuristics to reduce the number of gates in these circuits and we also propose an optimization algorithm for circuits of a few qubits. Concerning entanglement, we show how to create some useful entangled states when a circuit of CNOT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\texttt {CNOT}$$\end{document} gates acts on a fully factorized state. In the case of a 3-qubit system, we prove that a CNOT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\texttt {CNOT}$$\end{document} circuit acting on a fully factorized state can create all types of entanglement and we propose a method to evaluate the reliability of the implementation of a SLOCC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathtt {SLOCC}$$\end{document}-equivalent to the state |W3⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|\mathtt {W}_3\rangle $$\end{document} in a quantum machine by computing the value of the hyperdeterminant. In the case of a 4-qubit system, we propose a circuit to compute a generic entangled state and a (computer-assisted) proof of the impossibility of creating a SLOCC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathtt {SLOCC}$$\end{document}-equivalent to the state |W4⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|\mathtt {W}_4\rangle $$\end{document} from a circuit of CNOT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\texttt {CNOT}$$\end{document} gates acting on a factorized state

... As a unique quantum phenomenon, quantum entanglement is employed as an important resource to perform various quantum tasks securely, such as quantum key distribution (QKD) [1][2][3], quantum dense coding (QDC) [4][5][6], quantum teleportation (QT) [7][8][9], quantum secure direct communication (QSDC) [10,11], quantum secret sharing (QSS) [12][13][14], quantum operation teleportation (QOT) [15][16][17][18][19], remote state preparation (RSP) [20][21][22][23][24][25][26][27], quantum information concentration (QIC) [28][29][30], quantum entanglement purification (QEP) [31][32][33], and so on. Since the first theoretical scheme for transmitting an unknown single-qubit was proposed in 1993 [7], this technology has attracted much attention from researchers, and various theoretical and experimental QT schemes have been proposed [8,[34][35][36][37][38]. ...

... Fourth, qubit 1 continues to be sent to a Hadamard gate, and two CNOT gates are implemented on qubit pairs (1,3) and (2,4), respectively. The state |χ 3 can be transformed into ...

... This is the state as shown in Eq. (1). For the sake of simplicity, we omit its circuit diagrams. ...

The goal of this paper is to further study multi-party quantum communication of arbitrary single-qubit states. We first construct (2n+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(2n+1)$$\end{document}-qubit entangled channels via Hadamard gates and controlled-NOT gates and then propose two new (n+2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(n+2)$$\end{document}-party schemes for the quantum broadcast and multi-cast communications to guarantee that the sender can broadcast arbitrary complex coefficient single-qubit states to the n receivers, respectively, and synchronously under the control of the supervisor. In the first scheme, the quantum information transmitted synchronously comes from the same arbitrary complex coefficient single-qubit state, while the second scheme guarantees that the information is different among the n receivers to satisfy the requirement of the quantum multi-cast communications. Each scheme introduces auxiliary qubits and employs the feedforward strategy so that each receiver can successfully obtain the desired quantum state with success probability 100%. The feasibility of physical experiment, the security and the controller’s control power of the presented schemes are also discussed, repetitively.

... This trend can be viewed form the history of development of classical information technology over the past decades. In quantum internet, one can execute all kinds of quantum information tasks [8][9][10][11], such as securely transmitting information [1,3,[12][13][14][15][16][17], realizing distributed quantum computing [18,19], sharing enhanced sensing signals [20][21][22] and etc. Therefore, capable of realizing end-to-end entanglement distribution with good quality on arbitrary two or more users is a basic and core task for benchmarking a quantum internet. ...

... As the distance and the number of users increase, the connections between many quantum nodes form a large-scale quantum network on which quantum tasks can be executed, like quantum communications [1,3,[12][13][14][15][16][17], quantum computations [4,5,18,19,48] and quantum sensing [20][21][22]. Actually, today's quantum information tasks can be divided into two classes based on the use of quantum resource for building end-to-end quantum channel. ...

... Actually, today's quantum information tasks can be divided into two classes based on the use of quantum resource for building end-to-end quantum channel. One is single photon channel used for protocols like BB84 QKD [1] and Deng-Long04 quantum secure direct communication (QSDC) [14,15], and another one is entanglement whose applications include Ek-ert91 QKD [12], two-step QSDC [16,17], distributed quantum computing [18,19] and two/three-server blind quantum computing [48]. In practical experiments, single photon channel is easier than entanglement one, but in this article we mainly consider the entanglement network for two reasons. ...

With the rapid development of quantum information and technology in recent years, the construction of quantum internet for interconnecting all kinds of quantum devices, such as quantum processors and sensors, will be the next trend for practical quantum applications. In this paper, we propose the protocols for construction of connection-oriented and connectionless quantum networks by considering the concrete quantum repeater (QR) nodes. Four classes of QRs networks are considered first and designed with two types of protocols in link layer, i.e. simultaneous and one-by-one link. Based on those two link models, the connection-oriented protocol is presented for all classes of QRs networks and the connectionless protocol is proposed for the first, second and third classes QRs networks by only one-by-one link. Furthermore, we introduce a new hybrid connection model of quantum networks combined with connection-oriented and connectionless for practical uses. Our work is a new attempt to study the model of the network layer for different kinds of QR networks and paves the way for developing the protocol stack of universal large-scale quantum internet.

... By performing the secure quantum secret share protocol(QSSP) [44][45][46], Alice produces two l-bit private keys k AT and k AB shared with Tom and Bob, respectively, where l > > n. The QSSPs in [44,46] were unconditional secure due to the quantum no-cloning theorem and the impossibility of measuring the state of a quantum system simultaneously in two conjugate bases. ...

... The QSSPs in [44,46] were unconditional secure due to the quantum no-cloning theorem and the impossibility of measuring the state of a quantum system simultaneously in two conjugate bases. The security of Ekert's QSSP [45] was based on the famous Einstein-Podolsky-Rosen gedanken experiment and Bell's theorem (Clauser-Horne-Shimony-Holt inequalities). The adversary's eavesdropping will cause the measurement results violate Bell's theorem. ...

... For an ABQSS, it should guarantee the security of the signer's private key. In our ABQSS, the private keys are produced by performing the unconditionally secure QSSP [44][45][46][47][48]. Therefore, it is infeasible for the adversary to break the private keys during the initialization process of the scheme. ...

In this paper, a quantum signature scheme with semi-trusted arbitrator is proposed. In our scheme, the signatory encodes the classical message into non-orthogonal quantum sequence. Then, he generates the secret parameters with the key-controlled hash functions. The secret parameters are used to control the Pauli operation and Hadamard operation to encrypt the quantum message. After that the quantum message is entangled as the chained quantum sequence, which is used as the quantum signature. The quantum signature is verified by the chained decryption. The arbitrator and signature receiver need not perform the quantum swap test. The partners need not prepare the redundant decoy particles for the use of checking the quantum channel, because the disturbances can break the entangled chain such that the disturbed signature cannot pass the signature verification. Our scheme is secure against the forgery attack. Even the arbitrator cannot effectively forge a quantum signature. Therefore, the arbitrator can be semi-trusted. Our scheme has more advantages in security and efficiency than the similar arbitrated ones.

... This makes entanglement a invaluable resource that might beat classical resources in different communications contexts. Although it remained until the end of the last century the question of what entanglement is useful for, eventually entanglement has been harnessed to outperform classical communication protocols and to provide security for quantum key distribution [42,43] 5 . Specifically, quantum superdense coding [5] came against what was previously known in information theory to be a coding bound for classical information. ...

... Conversely, if Alice and Bob share apriori entanglement, a two-bit classical message can be sent through a single use of a quantum channel. Furthermore, this protocol has proved not to just outperform the performance of classical communication protocols, but also to be extremely secure [5,42,43]. But there is more to it. ...

... where I is the d × d identity matrix. By accounting for (42) with p = 1 2 , the Holevo information achievable through the quantum switch S ρc (N , M)(·) is given by: ...

In the theory of quantum communications, a deeper structure has been recently unveiled, showing that the capacity does not completely characterize the channel ability to transmit information due to phenomena – namely, superadditivity, superactivation and causal activation – with no counterpart in the classical world. Although how deep goes this structure is yet to be fully uncovered, it is crucial for the communication engineering community to own the implications of these phenomena for understanding and deriving the fundamental limits of communications. Hence, the aim of this treatise is to shed light on these phenomena by providing the reader with an easy access and guide towards the relevant literature and the prominent results from a communication engineering perspective.

... Such processes are impossible without the inclusion of entanglement. They have made entanglement a centerpiece in the current worldwide race toward both scientific and commercial exploitation of quantum processes, foretelling significant improvements in speed and security of communication and computing [10][11][12]. ...

... (iii and iv) Two distinct classes are genuinely entangled, the Greenberger-Horne-Zeilinger (GHZ) class and the W class (12). Those two individual states are themselves the most entangled states in each of those classes respectively. ...

... Those two individual states are themselves the most entangled states in each of those classes respectively. The W state is given in (12) and the GHZ state is ...

We introduce the challenges of multi-party quantum entanglement and explain a recent success in learning to take its measure. Given the widely accepted reputation of entanglement as a counter-intuitive feature of quantum theory, we first describe pure-state entanglement itself. We restrict attention to multi-party qubit states. Then we introduce the features that have made it challenging for several decades to extend an entanglement measure beyond the 2-qubit case of Bell states. We finish with a description of the current understanding that solves the 3-qubit entanglement challenge. This necessarily takes into account the fundamental division of the 3-qubit state space into two completely independent sectors identified with the so-called GHZ and $W$ states.

... Quantum entanglement is one of the most profound features of quantum mechanics [1]. It can be used to realize quantum tasks such as quantum communication [2][3][4], quantum simulation [5], quantum computation and so on [6]. How to characterize and quantify entanglement is one of the fundamental problems in quantum information [1] and many-body quantum physics [7]. ...

... where λ i and |x i are the eigenvalues and eigenvectors of M, respectively. The Schatten-p norm ( p ≥ 1) M p of M is given by 3 . It has been shown in [23] that M p satisfies the following matrix norm inequality, ...

Quantum entanglement is the core resource in quantum information processing and quantum computing. It is a significant challenge to effectively characterize the entanglement of quantum states. Recently, elegant separability criterion is presented by Elben et al. (Phys Rev Lett 125:200501, 2020) based on the first three partially transposed (PT) moments of density matrices. Then, Yu et al. (Phys Rev Lett 127:060504, 2021) proposed two general powerful criteria based on the PT moments. In this paper, based on the realignment operations of matrices we propose entanglement detection criteria in terms of such realignment moments. We show by detailed example that the realignment moments can also be used to identify quantum entanglement.

... Quantum Key Distribution describes a variety of techniques whereby quantum states are used to establish a shared random key between two spatially separated parties, commonly referred to as Alice and Bob in cryptographic parlance. BB84 30 is the most well-known QKD protocol, yet others exist which leverage different encoding schemes 31,32 as well as entanglement 33 . QKD is not a cryptographic mechanism-it is a method to distribute correlated random bit strings for later use in any application, including well-known symmetric cryptography schemes such as the Advanced Encryption Standard (AES), Blowfish, and others. ...

... QKD is not a cryptographic mechanism-it is a method to distribute correlated random bit strings for later use in any application, including well-known symmetric cryptography schemes such as the Advanced Encryption Standard (AES), Blowfish, and others. The commercial QKD system used in this paper implements an entanglement-based protocol 33 . It generates keys that are pulled into a higher layer to authenticate smart grid communications. ...

Smart grid solutions enable utilities and customers to better monitor and control energy use via information and communications technology. Information technology is intended to improve the future electric grid’s reliability, efficiency, and sustainability by implementing advanced monitoring and control systems. However, leveraging modern communications systems also makes the grid vulnerable to cyberattacks. Here we report the first use of quantum key distribution (QKD) keys in the authentication of smart grid communications. In particular, we make such demonstration on a deployed electric utility fiber network. The developed method was prototyped in a software package to manage and utilize cryptographic keys to authenticate machine-to-machine communications used for supervisory control and data acquisition (SCADA). This demonstration showcases the feasibility of using QKD to improve the security of critical infrastructure, including future distributed energy resources (DERs), such as energy storage.

... Quantum communication unlocks network applications that are provably impossible to realize using only classical communication. One striking example is secure communication using quantum key distribution [1,2], but many other applications are already known. Examples of these are secret sharing [3] and clock synchronization [4]. ...

... Since the Bell states are orthogonal to each other, it follows that p = 4 3 (1 − F em ) and that the corresponding probability of no-imperfection is 1 3 (4F em − 1). ...

We numerically study the distribution of entanglement between the Dutch cities of Delft and Eindhoven realized with a processing-node quantum repeater and determine minimal hardware requirements for verified blind quantum computation using group-IV color centers and trapped ions. Our results are obtained considering restrictions imposed by a real-world fiber grid and using detailed hardware-specific models. By comparing our results to those we would obtain in idealized settings we show that simplifications lead to a distorted picture of hardware demands, particularly on memory coherence and photon collection. We develop general machinery suitable for studying arbitrary processing-node repeater chains using NetSquid, a discrete-event simulator for quantum networks. This enables us to include time-dependent noise models and simulate repeater protocols with cut-offs, including the required classical control communication. We find minimal hardware requirements by solving an optimization problem using genetic algorithms on a high-performance-computing cluster. Our work provides guidance for further experimental progress, and showcases limitations of studying quantum-repeater requirements in idealized situations.

... Two of the earliest QKD protocols are BB84 [9] and E91 [10]. While the later uses entanglement, the former does not require it. ...

... E91 is also a QKD protocol proposed by Arthur K.Ekert in 1991, [10] which utilizes the idea of the Bell's Theorem [12] and Clauser-Horne-Shimony-Holt(CHSH) or Bell's Inequality [13].The EPR pair is used because of their entanglement properties, which are as follows: ...

Quantum cryptography was proposed as a counter to the capacity of quantum computers to break classical cryptosystems. A broad subclass of quantum cryptography, called quantum key distribution (QKD), relies on quantum mechanical process for secure distribution of the keys. Quantum channels are inherently noisy, and therefore these protocols will be susceptible to noise as well. In this paper, we study the performance of two QKD protocols - BB84 and E91 under thermal relaxation error. We show that while E91 protocol loses its security immediately due to loss of entanglement, the performance of BB84 protocol reduces to random guessing with increasing time. Next, we consider the action of an Eve on the BB84 protocol under thermal relaxation noise, who is restricted to guessing the outcome of the protocol only. Under this restriction, we show that Eve can still do better than random guessing when equipped with the characteristics of the noisy channel. Finally, we propose a modification of the BB84 protocol which retains the security of the original protocol, but ensures that Eve cannot get any advantage in guessing the outcome, even with a complete channel information.

... où le produit tensoriel |0⟩ A ⊗ |1⟩ B est écrit |0⟩ A |1⟩ B pour alléger les notations. Les états de Bell sont les états d'intrication bipartite maximale formant une base largement utilisée pour les codages denses en information quantique [117], pour la distribution de clef en cryptographie quantique [14,38], et dans des protocoles de téléportation dans l'élaboration de relais en télécommunication quantique [128]. ...

... La préparation ou la manipulation de ces états font intervenir un interféromètre de Mach Zehnder (MZI) déséquilibrés avec un bras plus long que l'autre tel que représenté en figure 3.1. L'avantage de ce type de codage pour des applications fibrées est que celui ci n'est pas sensible à la rotation de la polarisation dans la fibre lors de la propagation des qubits [14,38]. La génération de paires de photons intriqués en codage time-bin s'obtient ...

La lumière est un excellent candidat comme support d'information quantique en raison de la possibilité de réaliser des qubits optiques qui peuvent être transmis par des fibres optiques, manipulés au moyen de l'optique linéaire et interfacés avec la matière.La dualité onde-particule de la lumière a conduit à deux type d' encodages, traditionnellement séparés, de l'information quantique : une approche "à variables discrètes" (DV), basée par exemple sur des photons uniques, et une approche "à variables continues" (CV), qui repose sur des degrés de liberté continus tels que l'amplitude et la phase d'un champ lumineux.Les deux régimes présentent des avantages et des inconvénients spécifiques. L'approche DV a donné lieu à de nombreuses expériences révolutionnaires et permet de réaliser la téléportation avec une fidélité proche de l'unité, mais elle est dans la plupart des cas probabiliste et affectée par les limites des détecteurs de photons uniques. À l'inverse, l'approche CV peut bénéficier d'opérations inconditionnelles et d'une discrimination d'état non ambiguë, mais elle souffre d'une forte sensibilité aux pertes et de fidélités intrinsèquement limitées. Dans ce contexte, très récemment, l'hybridation entre les outils et concepts DV et CV a été envisagée comme une approche clé pour rassembler les avantages des deux régimes et contourner leurs limitations individuelles.Cette thèse s'inscrit dans cette démarche émergente mais potentiellement puissante. Plus précisément, elle explore l'intrication hybride entre des qubits optiques de type particule et de type onde. Cette ressource photonique complexe réunit les approches DV et CV et promet, entre autres, de transférer l'information d'un codage à l'autre. Dans la perspective d'applications futures des états hybrides aux communications longue distance sur fibres optiques et aux réseaux quantiques, la thèse se concentre en particulier sur l'étude et la réalisation d'états hybrides avec codage en time-bin sur le qubit de type particule. En time-bin, l'information est codée sur deux temps de génération/détection des photons. Par rapport aux autres approches, ce type d'encodage est particulièrement bien adapté à toute application impliquant des liaisons par fibre optique, car il est particulièrement robuste aux pertes et à la dispersion de polarisation. Dans le même esprit, la thèse explore également des ressources originales s'appuyant sur l'optique intégrée comme technologie habilitante pour la mise en œuvre future, hors laboratoire, de technologies quantiques basées sur l'intrication hybride.

... Introduction-Quantum entanglement is the striking feature of quantum states which exhibits correlations that cannot be accounted for classically. It is the fundamental resource and plays an important role in many quantum information processing such as quantum communications [1][2][3][4], quantum cryptography [5][6][7][8] and quantum computing [9][10][11]. Quantifying the entanglement has become a very important issue for both theoretical and potentially practical reasons. ...

Although quantum entanglement has already been verified experimentally and applied in quantum computing, quantum sensing and quantum networks, most of the existing measures cannot characterize the entanglement faithfully. In this work, by exploiting the Schmidt decomposition of a bipartite state $|\psi\rangle_{AB}$, we first establish a one-to-one correspondence relation between the characteristic polynomial of the reduced state $\rho_A$ and the polynomials its trace. Then we introduce a family of entanglement measures which are given by the complete eigenvalues of the reduced density matrices of the system. Specific measures called informationally complete entanglement measures (ICEMs) are presented to illustrate the advantages. It is demonstrated that such ICEMs can characterize finer and distinguish better the entanglement than existing well-known entanglement measures. They also give rise to criteria of state transformations under local operation and classical communication. Moreover, we show that the ICEMs can be efficiently estimated on a quantum computer. The fully separability, entanglement and genuine multipartite entanglement can detected faithfully on quantum devices.

... Quantum key distribution (QKD) [1,2] can distribute information-theoretic secret keys between two legitimate peers Alice and Bob, even in the presence of an eavesdropper Eve. Owing to the advantage of the theoretic security, lots of QKD demonstrations with high rate and long distance have been reported [3][4][5][6][7]. ...

Phase-matching quantum key distribution (PM-QKD) provides a promising solution to surpass the fundamental rate-distance bound without quantum repeaters. In this paper, we insert an additional advantage distillation step after quantum communication to further improve the performance of PM-QKD. Simulation results show that, by splitting the raw key into blocks of only a few bits so as to identify highly correlated bit pairs, the advantage distillation method can tolerate high system misalignment errors and improve the secret key rate and transmission distance significantly, which is very promising in current PM-QKD systems.

... Quantum communication has been expanded from the initially proposed bi-partite key exchange [1,2] to networked settings [3][4][5][6]. One particularly interesting application of quantum networks is conference key agreement [7,8]. ...

Multipartite entanglement enables secure and anonymous key exchange between multiple parties in a network. In particular Greenberger-Horne-Zeilinger (GHZ) states have been introduced as resource states for anonymous key exchange protocols, in which an anonymous subset of parties within a larger network establishes a secret key. However, the use of other types of multipartite entanglement for such protocols remains relatively unexplored. Here we demonstrate that linear cluster states can serve as a versatile and potentially scalable resource in such applications. We implemented an anonymous key exchange protocol with four photons in a linear cluster state and established a shared key between three parties in our network. We show how to optimize the protocol parameters to account for noise and to maximize the finite key rate under realistic conditions. As cluster states have been established as a flexible resource in quantum computation, we expect that our demonstration provides a first step towards their hybrid use for networked computing and communication.

... In recent decades, the development of photonic quantum technologies [30] has expanded the quantum information ecosystem, particularly in the fields of quantum communication and quantum sensing. Quantum communication has many potential applications, including clock synchronization [31] and encrypted communication [32], [33]. Central to these applications is a quantum photonic network enabling the transmission and entanglement of quantum bits (qubits) over long distances [34]. ...

Integrated quantum photonics devices in diamond have tremendous potential for many quantum applications, including long-distance quantum communication, quantum information processing, and quantum sensing. These devices benefit from diamond's combination of exceptional thermal, optical, and mechanical properties. Its wide electronic bandgap makes diamond an ideal host for a variety of optical active spin qubits that are key building blocks for quantum technologies. In landmark experiments, diamond spin qubits have enabled demonstrations of remote entanglement, memory-enhanced quantum communication, and multi-qubit spin registers with fault-tolerant quantum error correction, leading to the realization of multinode quantum networks. These advancements put diamond at the forefront of solid-state material platforms for quantum information processing. Recent developments in diamond nanofabrication techniques provide a promising route to further scaling of these landmark experiments towards real-life quantum technologies. In this paper, we focus on the recent progress in creating integrated diamond quantum photonic devices, with particular emphasis on spin-photon interfaces, cavity optomechanical devices, and spin-phonon transduction. Finally, we discuss prospects and remaining challenges for the use of diamond in scalable quantum technologies.

... Initially, QKD protocols relied on polarization-entangled photons [3]. Alice and Bob could extract a single key bit by measuring the polarization of entangled photon pairs. ...

We develop new methods of quantifying the impact of photon detector imperfections on achievable secret key rates in Time-Entanglement based Quantum Key Distribution (QKD). We address photon detection timing jitter, detector downtime, and photon dark counts and show how each may decrease the maximum achievable secret key rate in different ways. We begin with a standard Discrete Memoryless Channel (DMC) model to get a good bound on the mutual information lost due to the timing jitter, then introduce a novel Markov Chain (MC) based model to characterize the effect of detector downtime and show how it introduces memory to the key generation process. Finally, we propose a new method of including dark counts in the analysis that shows how dark counts can be especially detrimental when using the common Pulse Position Modulation (PPM) for key generation. Our results show that these three imperfections can significantly reduce the achievable secret key rate when using PPM for QKD. Additionally, one of our main results is providing tooling for experimentalists to predict their systems' achievable secret key rate given the detector specifications.

... A positive answer would mean that quantum mechanics is an incomplete theory, so sub-quantum levels of reality are in principle possible (Einstein et al. 1935;Bohm 1951Bohm , 1952Bell 1964). These deeper levels of reality could, at least theoretically, be used to hack quantum communication systems (Bennett and Brassard 1984;Ekert 1991;Bennett et al. 1992;Gisin et al. 2002;Zhao et al. 2008;Gerhardt et al. 2011). ...

Local hidden-variable model of singlet-state correlations discussed in Czachor (Acta Phys Polon A 139:70, 2021a) is shown to be a particular case of an infinite hierarchy of local hidden-variable models based on an infinite hierarchy of calculi. Violation of Bell-type inequalities can be interpreted as a ‘confusion of languages’ problem, a result of mixing different but neighboring levels of the hierarchy. Mixing of non-neighboring levels results in violations beyond the Tsirelson bounds.

... Polarization is a paradigmatic two-dimensional photonic DOF that allowed for pioneering demonstrations in quantum information, ranging from fundamental tests of quantum mechanics [3] to quantum computing [4] and communication tasks [5,6]. Focusing on DV encoding, polarization Bell states, such as |Ψ + polar = (|H |V + |V |H ) / √ 2, where H and V stand for the horizontal and vertical polarizations of single photons, constitute a fundamental building block for many of these applications. ...

We demonstrate a chip-integrated semiconductor source that combines polarization and frequency entanglement, allowing the generation of entangled biphoton states in a hybrid degree of freedom without postmanipulation. Our AlGaAs device is based on type-II spontaneous parametric down-conversion (SPDC) in a counterpropagating phase-matching scheme, in which the modal birefringence lifts the degeneracy between the two possible nonlinear interactions. This allows the direct generation of polarization-frequency entangled photons, at room temperature and telecom wavelength, and in two distinct spatial modes, offering enhanced flexibility for quantum information protocols. The state entanglement is quantified by a combined measurement of the joint spectrum and Hong-ou-Mandel interference of the biphotons, allowing to reconstruct a restricted density matrix in the hybrid polarization-frequency space.

... In quantum communications, entanglement is central to the implementation of cryptographic tasks such as entanglement-based quantum key distribution [28]. Very interestingly, untrusted sources or detection apparatus can be tested by implementing some Bell tests [88,89,90], thus providing unconditionally secure -although experimentally very challenging -device-independent protocols. Finally entanglement is fundamental for the establishment of long-distance communication in quantum networks, as introduced in the following sections. ...

This thesis focuses on the implementation of quantum teleportation-based protocols involving conjointly the discrete- and continuous-variable approaches of optical quantum information processing. We first present the interest of these protocols in the framework of heterogeneous quantum networks, and we introduce the experimental techniques for the generation of non-Gaussian quantum states such as single photons, optical Schrödinger cat states, up to hybrid entanglement between discrete- and continuous-variable quantum states. We develop a novel experimental tool for the implementation of a Bell-state measurement composed of photon counting and quadrature selection. By combining these methods, we demonstrate an entanglement swapping protocol between two entangled states of different natures: single-photon entanglement and hybrid entanglement of light. We describe the installation of an additional heralded single-photon source and a cryogenic system for the operation of superconducting single-photon detectors. We finally employ these new resources in a hybrid quantum teleportation protocol which enables the conversion of quantum information from discrete- to continuous-variables. This work paves the way towards the interconnection of platforms of different natures in heterogeneous quantum networks.

... The quantum operations and usage of Alice's encoding states on two paired locations(1,2). ...

Quantum key distribution — the establishment of information-theoretically secure keys based on quantum physics — is mainly limited by its practical performance, which is characterised by the dependence of the key rate on the channel transmittance R(η). Recently, schemes based on single-photon interference have been proposed to improve the key rate to R=O(η) by overcoming the point-to-point secret key capacity bound with interferometers. Unfortunately, all of these schemes require challenging global phase locking to realise a stable long-arm single-photon interferometer with a precision of approximately 100 nm over fibres that are hundreds of kilometres long. Aiming to address this problem, we propose a mode-pairing measurement-device-independent quantum key distribution scheme in which the encoded key bits and bases are determined during data post-processing. Using conventional second-order interference, this scheme can achieve a key rate of R=O(η) without global phase locking when the local phase fluctuation is mild. We expect this high-performance scheme to be ready-to-implement with off-the-shelf optical devices. Measurement-device-independent QKD schemes suffer from a trade-off between ease of implementation (avoiding the need for global phase locking) and high rates (quadratic improvement in rate). Here, the authors propose a protocol which offers both simple implementation and strong performances.

... However, as Shor's algorithm can factorize large numbers in essentially polynomial time, the realization of quantum computer will be a threat to classical cryptography [1,2]. The security issue has been addressed by quantum key distribution (QKD) that enables two remote users to share secret keys [3,4], whose unconditional security was theoretically proved in Refs. [5,6]. ...

A controlled quantum secure direct communication protocol with authentication based on quantum search algorithm is put forward, consisting of three participants: a sender, a receiver and one controller. Two unitary operators Uw and US in quantum search algorithm are used to encode classical bits and decode information, respectively, and the decoy photons based on identity sequences are adopted to detect the channel security and authenticate the identity of the communication parties. The secret message can be reconstructed successfully with the help of the controller. Moreover, the security analysis reveals that this protocol can not only effectively prevent the eavesdropper from stealing useful information but also discover the eavesdropping behavior. Compared with the existing QSDC protocols with quantum search algorithm, the proposed one has the advantages of identity authentication of the communicators, detecting man-in-the-middle attack and the attack from dishonest controller, and its qubit efficiency can reach as high as 25%.

... Digital signature based on public-key cryptosystems has been widely used in the modern online information transmission, for example, electronic elections, digital cash, etc., to provide entity authentication and non-repudiation, message integrity and confidentiality. The original research of public-key digital signature is focused on the schemes upon the computationally hard number theoretic problems, such as RSA designed on the difficulty assumption of factoring large integers (Rivest et al. 1978), ElGamal designed on the difficulty assumption of discrete logarithms, etc. (ElGamal 1985) But the development of quantum computer has shocked our confidence on this kind of classical digital signature schemes (Gisin et al. 2002;Bennett et al. 1992;Bernstein 2009;Brassard et al. 2000;Ekert 1991;Bennett 1992;Gröblacher et al. 2006), by applying "Shor's algorithm" (Shor 1999), theoretic problems will no longer be hard and classical cryptosystems can be broken easily. We can only achieve computational security by improving the related parameters in scale, it is dynamically affected by the development of number theory and computing performance, as a result, it lacks sustainedly durable security. ...

The current development toward quantum attack has shocked our confidence on classical digital signature schemes. As one of the mainstreams of post quantum cryptography primitives, hash-based signature has attracted more and more concern in both cryptographic research and application in recent years. The goal of this paper is to present, classify and discuss different solutions for hash-based signature. Firstly, this paper discusses the research progress in the component of hash-based signature, i.e., one-time signature and few-time signature; then classifies the tree-based public key authentication schemes of hash-based signature into limited number and stateful schemes, unlimited number and stateful schemes and unlimited number and stateless schemes. The above discussion aims to analyze the overall design idea of different categories of hash-based signatures, as well as the construction, security reduction and performance efficiency of specific schemes. Finally, the perspectives and possible development directions of hash-based signature are briefly discussed.

... Quantum key distribution (QKD) uses quantum theory to achieve theoretically unconditional and secure communication between long-distance parties [1][2][3][4]. The use of quantum repeaters can break the theoretical upper limit of transmission distance, but quantum repeater schemes are not yet mature [5,6]. ...

Twin-field quantum key distribution (TF-QKD) can overcome the basic limits of QKD without repeaters. In practice, TF-QKD needs to optimize all parameters when limited data sets are considered. The traditional exhaustive traversal or local search algorithm can’t meet the time and resource requirements of the real-time communication system. Combined with machine learning, parameter optimization prediction of QKD has become the mainstream of parameter optimization. Random forest (RF) is a classical algorithm of the bagging class in integrated learning, and back-propagation neural network (BPNN) is an important algorithm in the neural network. This paper uses the extreme gradient boosting (XGBoost) of boosting class to predict the optimization parameters of TF-QKD and compares it with RF and BPNN. The results show that XGBoost can efficiently and accurately predict optimization parameters, and its performance is slightly better than RF and BPNN in parameter prediction, which can provide a reference for future real-time QKD networks.

... Quantum correlations have been intensively studied in recent decades as a fundamental resource in quantum information theory such as quantum teleportation [1], quantum computation [2], quantum communication [3], and so forth [4,5]. Quantum correlations reveal non-classical aspects of quantum mechanics, which has no classical counterpart. ...

The isotropic Heisenberg two-spin-1/2 model in the XXX configuration under an external transverse nonuniform magnetic field is considered at thermal equilibrium. In the context of the Heitler–London approach, the variation of the spin–spin exchange coupling strength in terms of the position is adopted. The effects of the inter-spin relative coupling distance r and nonuniform magnetic field on the thermal evolution of quantum correlations are studied in detail. By tuning the coupling distance r, temperature T and nonuniform magnetic field B, quantum correlations can be scaled in the bipartite system. Astonishingly, we find the long sustainable behavior of geometric quantum discord in comparison with entanglement over the coupling distance r. Moreover, we show the existence of separable quantum states with nonzero quantum correlations in terms of trace discord. Besides, the quantum correlations shared between the considered bipartite system parts are only the entanglement type for a fixed temperature and suitable strong nonuniform magnetic field values. An entangled-unentangled phase transition at T=0.1 with threshold relative distance r_f can be detected by the entanglement behavior in terms of B and r. A kind of correspondence between thermal entanglement and thermal non-classical correlations for a strong value of B can be observed. It is our hope that this research may open a new path to consider the role of Heitler–London approach in non-classical correlations preservation.

... Therefore, how to realize the secure transmission of information is an important development direction in modern communication. Quantum key distribution (QKD) [1,2,3,4,5] combined with the One-time pad (OTP) can achieve theoretically unconditional secure communication. It can be implemented in the discrete-variable scheme and continuousvariable scheme (CVQKD) [6,7], and the latter has the advantages of a high secret key rate (SKR) and low cost. ...

Excess noise is a major obstacle to high-performance continuous-variable quantum key distribution (CVQKD), which is mainly derived from the amplitude attenuation and phase fluctuation of quantum signals caused by channel instability. Here, an excess noise suppression scheme based on equalization is proposed. In this scheme, the distorted signals can be corrected through equalization assisted by a neural network and pilot tone, relieving the pressure on the post-processing and eliminating the hardware cost. For a free-space channel with more intense fluctuation, a classification algorithm is added to classify the received variables, and then the distinctive equalization correction for different classes is carried out. The experimental results show that the scheme can suppress the excess noise to a lower level, and has a significant performance improvement. Moreover, the scheme also enables the system to cope with strong turbulence. It breaks the bottleneck of long-distance quantum communication and lays a foundation for the large-scale application of CVQKD.

... model. The QKD protocol that we propose is different from the BB84 protocol [34], the decoy-state protocol [35,36], and the generic entangle-based state protocol [37,38]. Due to the short-range entanglement between adjacent subsystems of the MPS state, we can compress these subsystems to obtain a long-range entanglement leaving a shortrange entanglement unchanged by using the local compression protocol proposed by Bai et al. [39]. ...

Almost currently published quantum key distribution (QKD) protocols are variants of the first protocol proposed by Bennett and Brassard, and the generic entanglement-based protocol. These protocols, however, are not very efficient. An improvement of key generation rate is possible by using quantum many-body systems, and tensor network states provides a compact model for them. The work presents an improved QKD protocol, which first uses partial isometries to compress a matrix product state (MPS) |Ψ⟩ into its compressed MPS |Ψ(n)⟩. Then, Alice uses |Ψ(n)⟩ to communicate with Bob via a quantum channel. Next, Alice transmits the number of compressed operations to Bob via a secure classical channel. Finally, according to the measured results, Alice and Bob share a cryptographic key from the MPS |Ψ⟩. Our protocol can obtain a higher key generation capability and a longer communication distance. We apply the flow network model to obtain the upper bound of the dimension of the geometric index.

... In addition to the above fundamental tools, quantum key distribution (QKD) protocols [34][35][36] are also used to securely distribute keys in quantum signature schemes [37,38]. ...

Based on quantum asymmetric cryptosystem, a public-key quantum signature for classical messages is proposed. In our scheme, the private key is randomly chosen by signer, and the public key is generated by the trusted key generator using the quantum one-way function. The signer signs a message with the private key, while the verifier can use the public key to verify the quantum signature without the help of third party. The signer’s key pair can be reused. Hence, our scheme can simplify the key management of the quantum signature system. Security analysis results show that the proposed scheme satisfies unforgeability and non-repudiation. All the algorithms in our scheme are public. Compared to similar schemes, ours is relatively more secure and can be easily applied to practical scenarios.

... Quantum information processing is responsible for implementing tasks such as super dense coding [1], teleportation [2] and key generation [3]. Quantum entanglement is one of the key reasons [4] of quantum advantages and has many applications ranging from quantum teleportation to quantum cryptography [5]. ...

Entanglement as a vital resource for information processing can be described by special properties of the quantum state. Using the well-known Weyl basis we propose a new Bloch decomposition of the quantum state and study its separability problem. This decomposition enables us to find an alternative characterization of the separability based on the correlation matrix. We shaw that the criterion is effective in detecting entanglement for the isotropic states, Bell-diagonal states and some PPT entangled states. We also use the Weyl operators to construct an detecting operator for quantum teleportation.

... Entanglement has several applications [35]: information coding [36], teleportation [37][38][39][40][41], cryptography [42][43][44], quantum computing [45], entanglement swapping [46][47][48][49][50]. The environment can be defined as being a medium made up of a set of elements that can influence our system. ...

A comparative study of the dynamics of entanglement purity and degree of purity in two hybrid quantum systems under the effect of a Markovian and non-Markovian regime of a random telegraph noise is presented. The first system contains two qubits and one qutrit, while the second system contains one qubit and two qutrits. In addition, each system presents three configurations: the different, the common and the bipartite environment. In the bipartite environment, we have three cases depending on whether two subsystems are in the same environment and one subsystem in its environment alone. We found that in all these configurations, the same behavior is observed for negativity, purities and degrees of purity. The lower the purity, the more the degree of purity becomes and the system is less influenced by environmental corruption. Purity decreases more in the second system than in the first system and we can conclude that the second system preserves quantum properties better than the first and we also come to the conclusion that a common environment is more robust to the effects of random telegraph noise than a bipartite environment case3 which is more robust than the bipartite environment case2 which is also more robust than the bipartite environment case1 which is more robust than the different environment.

... In 1984, Bennett and Brassard proposed the first quantum key distribution (QKD) protocol [1], based on Wiesner's theory of quantum conjugate coding [2], and this is the first protocol of quantum cryptography. Since then, QKD has received extensive attention both theoretically [3][4][5][6] and experimentally [7][8][9][10][11]. ...

Quantum secure direct communication (QSDC) and deterministic secure quantum communication (DSQC) are two important branches of quantum cryptography, where one can transmit a secret message securely without encrypting it by a prior key. In the practical scenario, an adversary can apply detector-side-channel attacks to get some non-negligible amount of information about the secret message. Measurement device–independent (MDI) quantum protocols can remove this kind of detector-side-channel attacks, by introducing an untrusted third party, who performs all the measurements during the protocol with imperfect measurement devices. In this paper, we put forward the first MDI-QSDC protocol with user identity authentication, where both the sender and the receiver first check the authenticity of the other party and then exchange the secret message. Then, we extend this to an MDI quantum dialogue protocol, where both the parties can send their respective secret messages after verifying the identity of the other party. Along with this, we also report the first MDI-DSQC protocol with user identity authentication. Theoretical analyses prove the security of our proposed protocols against common attacks.

... Today, this crucial task faces major challenges from quantum-based attacks and implementation vulnerabilities. A promising solution is to use quantum key distribution (QKD), which uses the laws of quantum physics to assess eavesdropping attempts on the public channel 16,17 . However, in its standard form, QKD is prone to implementation side channels, like all modern information systems 13,18 . ...

Device-independent quantum key distribution (DIQKD) enables the generation of secret keys over an untrusted channel using uncharacterized and potentially untrusted devices1–9. The proper and secure functioning of the devices can be certified by a statistical test using a Bell inequality10–12. This test originates from the foundations of quantum physics and also ensures robustness against implementation loopholes13, thereby leaving only the integrity of the users’ locations to be guaranteed by other means. The realization of DIQKD, however, is extremely challenging—mainly because it is difficult to establish high-quality entangled states between two remote locations with high detection efficiency. Here we present an experimental system that enables for DIQKD between two distant users. The experiment is based on the generation and analysis of event-ready entanglement between two independently trapped single rubidium atoms located in buildings 400 metre apart14. By achieving an entanglement fidelity of ℱ≥0.892(23) and implementing a DIQKD protocol with random key basis15, we observe a significant violation of a Bell inequality of S = 2.578(75)—above the classical limit of 2—and a quantum bit error rate of only 0.078(9). For the protocol, this results in a secret key rate of 0.07 bits per entanglement generation event in the asymptotic limit, and thus demonstrates the system’s capability to generate secret keys. Our results of secure key exchange with potentially untrusted devices pave the way to the ultimate form of quantum secure communications in future quantum networks. A system based on trapped rubidium atoms for generating quantum secure keys between distant users is presented, which could operate in a device-independent fashion.

... T HE unconditional security offered by quantum key distribution (QKD) relies on laws of quantum physics [1], [2], which dictate that any attempt by an adversary to know about the secret key, would inevitably introduce disturbance that alerts the legitimate parties [3], [4]. This ultimate informationtheoretic security has been proved for idealized devices [4]- [6] and also under semi-realistic conditions [7]- [9]. ...

Practical implementations of quantum key distribution (QKD) have been shown to be subject to various detector side-channel attacks that compromise the promised unconditional security. Most notable is a general class of attacks adopting the use of faked-state photons as in the detector-control and, more broadly, the intercept-resend attacks. In this paper, we present a simple scheme to overcome such class of attacks: A legitimate user, Bob, uses a polarization randomizer at his gateway to distort an ancillary polarization of a phase-encoded photon in a bidirectional QKD configuration. Passing through the randomizer once on the way to his partner, Alice, and again in the opposite direction, the polarization qubit of the genuine photon is immune to randomization. However, the polarization state of a photon from an intruder, Eve, to Bob is randomized and hence directed to a detector in a different path, whereupon it triggers an alert. We demonstrate theoretically and experimentally that, using commercial off-the-shelf detectors, it can be made impossible for Eve to avoid triggering the alert, no matter what faked-state of light she uses.

... Consequently, quantum algorithms must exploit high amounts of entanglement to reach higher possible capabilities than classical algorithms. This entanglement property has applications in many aspects of quantum computing, such as cryptography (Ekert, 1991), and quantum computation (Nielsen and Chuang, 2002;Shor, 1999). ...

Quantum computing is a rapidly growing field attracting the interest of both researchers and software developers. Supported by its numerous open-source tools, developers can now build, test, or run their quantum algorithms. Although the maintenance practices for traditional software systems have been extensively studied, the maintenance of quantum software is still a new field of study but a critical part to ensure the quality of a whole quantum computing system. In this work, we set out to investigate the distribution and evolution of technical debts in quantum software and their relationship with fault occurrences. Understanding these problems could guide future quantum development and provide maintenance recommendations for the key areas where quantum software developers and researchers should pay more attention. In this paper, we empirically studied 118 open-source quantum projects, which were selected from GitHub. The projects are categorized into 10 categories. We found that the studied quantum software suffers from the issues of code convention violation, error-handling, and code design. We also observed a statistically significant correlation between code design, redundant code or code convention, and the occurrences of faults in quantum software.

... In addition to the above fundamental tools, quantum key distribution (QKD) protocols [7,33,34] are used to securely distribute keys in quantum cheque schemes [20][21][22][23]. Public-key quantum digital signatures based on quantum one-way function are also used in our scheme for the signing and verification of the quantum cheque. ...

Based on the quantum public-key cryptosystem, a transferable quantum cheque scheme is proposed. In our scheme, the bank is a trusted third party who acts as a key generation center and issues quantum blank cheque. The payer makes a payment to the payee by signing the quantum cheque with the private key, and the payee can verify the cheque with the payer’s public key locally. The cheque can be transferred many times between different customers. The transfer and verification phases do not require the help of the bank. Hence, the cheque needs to be cleared only once, which reduces the workload on the bank. Security analysis results show that the proposed quantum cheque scheme is impossible to forge, double spend and repudiate.

... Entanglement is widely recognized as one of the most important resources in quantum information processing. Maximally entangled states have been applied to various information-processing tasks, including quantum communication channels [1], quantum cryptography [2], quantum teleportation [3], and so on. Entanglement detection is one of the open questions in quantum information theory. ...

It is well known that one can extract all the information of an unknown quantum channel by means of quantum process tomography, such as standard quantum-process tomography and ancilla-assisted quantum process tomography (AAQPT). Furthermore, it has been shown that entanglement is not necessary for AAQPT, there exist separable states which are also useful for it. Surprisingly, in this work we find that not all entangled states are useful for AAQPT, there also exist some entangled states which are useless. The realignment operation used in entanglement detection can be related to the question whether a bipartite state is useful for AAQPT. We derive the relationship between them and show the process of extracting the complete information of an unknown channel by the realignment operation. Based on this relationship, we present examples of a two-qutrit entangled state and a two-qutrit bound entangled state. Both of these two examples are entangled but they cannot be used for AAQPT. Last but not least, experimental verification has also been performed on the IBM platform.

... Driven by the growing demand for a high secure communication system, quantum key distribution (QKD) that is based on quantum laws is regarded as an essential element of the future quantum safe infrastructure including quantum-resistant classical algorithms and quantum cryptographic solutions (Diamanti et al., 2016). Firstly proposed by Ekert, 1991 andBennett, Brassard, andMermin, 1992, entangled photon source is a promising solution for QKD owing to its high tolerance for channel loss and high robustness to environmental fluctuations (Yin et al., 2017). In 2018, the first intercontinental quantum-secured communication based on QKD was realized with Chinese satellite Micius (S.-K. ...

Silicon photonics is promising for high-speed communication systems, short-reach optical interconnects, and quantum technologies. Direct epitaxial growth of III-V materials on silicon is also an ideal solution for the next generation of photonic integrated circuits (PICs). In this context, quantum-dots (QD) lasers with atom-like density of states are promising to serve as the on-chip laser sources, owing to their high thermal stability and strong tolerance for the defects that arise during the epitaxial growth. The purpose of this dissertation is to investigate the nonlinear properties and dynamics of QD lasers on Si for PIC applications. The first part of this thesis investigates the dynamics of epitaxial QD lasers on Si subject to external optical feedback (EOF). In the short-cavity regime, the QD laser exhibits strong robustness against parasitic reflections hence giving further insights for developing isolator-free PICs. In particular, a near-zero linewidth enhancement factor is crucial to achieve this goal. The second part is devoted to studying the static properties and dynamics of a single-frequency QD distributed feedback (DFB) laser for uncooled and isolator-free applications. The design of a temperature-controlled mismatch between the optical gain peak and the DFB wavelength contributes to improving the laser performance with the increase of temperature. The third part of this dissertation investigates the QD-based optical frequency comb (OFC). External control techniques including EOF and optical injection are used to optimize the noise properties, reduce the timing-jitter, and increase the frequency comb bandwidth. In the last part, an investigation of the optical nonlinearities of the QD laser on Si is carried out by the four-wave mixing (FWM) effect. This study demonstrates that the FWM efficiency of QD laser is more than one order of magnitude higher than that of a commercial quantum-well laser, which gives insights for developing self-mode-locked OFCs based on QD. All these results allow for a better understanding of the nonlinear dynamics of QD lasers and pave the way for developing high-performance classical and quantum PICs on Si.

... Indeed, quantum information processing offers many significant advantages over classical processing, for example, high-speed computing with higher precision and accuracy. In this regard, quantum entanglement remains a fundamental and extremely valuable ingredient in the development of emerging quantum technologies including quantum teleportation [1,2], quantum cryptography [3,4], and quantum protocols [5,6]. Despite all its potential, it is still clunky to measure and characterize entanglement and quantum correlations in quantum systems comprised of many parties. ...

We address the dynamics of quantum coherence and non-classical correlations in a two-qubit one-dimensional XXZ Heisenberg spin-12 chain when exposed to a homogeneous magnetic field and characterized by the combined effects of temperature, Dzyaloshinsky–Moriya (DM), Kaplan–Shekhtman–Entin–Wohlman–Aharony (KSEA) interactions. Using local quantum uncertainty, we estimate quantum correlations in the considered thermal state, whereas quantum coherence is measured using ℓ1 norm of coherence and relative entropy of coherence. We show that the qualitative as well as the quantitative features of the quantum correlations and coherence depend largely upon the parameters of the two-qubit spin-chain and magnetic field. Quantum correlations and coherence in spin chains have distinct natures and behave differently, which we find intriguing. The ℓ1 norm of coherence was shown to be more dependable than the relative entropy of coherence for quantifying coherence. The dynamical behavior of quantum correlations and coherence has been proven to be largely non-oscillatory. We further show that depending on the temperature, DM, and KSEA interaction strengths, not only can the coherence and non-classical correlations be preserved, but that the initial mixed states can be readily transformed into maximally correlated and coherent states

... The last three decades have witnessed a burgeoning interest in study of quantum communication, quantum computation and, quantum search, to name a few [1][2][3][4][5] . The interest largely owes to a promise of outperforming their classical counterparts, or proposals of altogether novel applications not possible with purely classical resources. ...

Near-term quantum communication protocols suffer inevitably from channel noises, whose alleviation has been mostly attempted with resources such as multiparty entanglement or sophisticated experimental techniques. Generation of multiparty higher dimensional entanglement is not easy. This calls for exploring realistic solutions which are implementable with current devices. Motivated particularly by the difficulty in generation of multiparty entangled states, in this paper, we have investigated error-free information transfer with minimal requirements. For this, we have proposed a new information encoding scheme for communication purposes. The encoding scheme is based on the fact that most noisy channels leave some quantities invariant. Armed with this fact, we encode information in these invariants. These invariants are functions of expectation values of operators. This information passes through the noisy channel unchanged. Pertinently, this approach is not in conflict with other existing error correction schemes. In fact, we have shown how standard quantum error-correcting codes emerge if suitable restrictions are imposed on the choices of logical basis states. As applications, for illustration, we propose a quantum key distribution protocol and an error-immune information transfer protocol.

Encoding computing qubits in multiple degrees of freedom (DOFs) of a photonic system allows hyperparallel quantum computation to enlarge channel capacity with less quantum resource, and constructing high-fidelity hyperparallel quantum gates is always recognized as a fundamental prerequisite for hyperparallel quantum computation. Herein, we propose an approach for implementing a high-fidelity photonic hyperparallel controlled-phase-flip (CPF) gate working with polarization, spatial-mode, and frequency DOFs, through utilizing the practical interaction between the single photon and the diamond nitrogen vacancy (NV) center embedded in the cavity. Particularly, the desired output state of the gate without computation errors coming from the practical interaction is obtained, and the robust fidelity is guaranteed in the nearly realistic condition. Meanwhile, the requirement for the experimental realization of the gate is relaxed. In addition, this approach can be generalized to complete the high-fidelity photonic three-DOF hyperparallel CPF N gate and parity-check gate. These interesting features may make the present scheme have potential for applications in the hyperparallel quantum computation.

Quantum key distribution offers the possibility of cryptography whose security is demonstrated by the laws of quantum physics. The first commercial systems of this technology are now available. This thesis focuses on continuous variable protocols, whose practical implementation is close to modern digital transmission techniques over optical fibers. By exploiting these techniques, we realize an experimental system for high speed continuous variable quantum key distribution.

In the satellite-ground quantum key distribution network for electric IoT, the transmitted data may have errors caused by the external environment and equipment. In order to ensure the correctness and consistency of the transmitted data, we propose a data reconciliation model based on quantum low density parity check (QLDPC) code for satellite-ground quantum key distribution network. We perform the check operator of QLDPC on the obtained raw keys, and use belief propagation algorithm and ordered statistics decoding technology to implement error correction. Compared with MET-LDPC and Turbo code, our model based on QLDPC has higher error correction efficiency with the increase of bit error rate.

Double quantum dot (DQD) system is an ideal candidate for qubit in quantum information theory. Hence, we will investigate the two couple DQDs in the presence of intrinsic decoherence. We derive the energy spectrum and the corresponding eigenstates. Using the concurrence as a measure of entanglement for a bipartite pure state, the entanglement of the energy eigenstates is obtained and shows that the energy eigenstates reduce to the Bell states for Δ1=Δ2=0. The effects of the physical parameters such as tunneling rate between two QDs, Coulomb coupling, and intrinsic decoherence on the entanglement and the dynamics of DQD system will be examined. Furthermore, fidelity is used to measure how close the dynamically evolved state is to the initial state. It is found that for a given Γ and the smaller (larger) values of Δ2 (coulomb potential), the DQD system is more robust to the destructive effect of the intrinsic decoherence.

A research roadmap for quantum computation (2004).

This chapter is devoted to the fundamentals of quantum key distribution (QKD). The chapter begins with a description of key differences between conventional cryptography and QKD. In the section on QKD basics, we review various types of QKD. We then describe two fundamental theorems on which QKD relies: the no-cloning theorem and the theorem of the inability to unambiguously distinguish nonorthogonal quantum states. In the section on discrete-variable QKD (DV-QKD) systems, we describe BB84, B92, Ekert (E91), Einstein–Podolsky–Rosen (EPR), and time-phase encoding protocols. In the section on QKD security, the secret-key rate (SKR) is represented as the product of the raw key rate and fractional rate. A generic expression for fractional rate is provided, followed by a description of different eavesdropping strategies, including individual, collective, coherent, and quantum hacking/side-channel attacks. For individual and coherent attacks, corresponding secret fraction expressions are provided. Decoy-state protocols are then described together with the corresponding SKR calculation. Next, key concepts for measurement-device-independent QKD (MDI-QKD) protocols are introduced, including polarization-based and time-phase encoding-based MDI-QKD protocols as well as secrecy fraction calculations. Further, twin-field QKD protocols are described, and their performance is evaluated against decoy-state and MDI-QKD protocols. The focus then moves to information reconciliation and privacy amplification steps. In the section on continuous-variable QKD (CV-QKD) protocols, homodyne and heterodyne detection schemes are described first, followed by a brief description of squeezed state-based protocols. Coherent states are much easier to generate and manipulate, so coherent state-based protocols are described in detail. For lossy transmission channels, corresponding covariance matrices are derived for homodyne and coherent detections schemes, followed by SKR derivation for prepare-and-measure Gaussian modulation-based CV-QKD. Some illustrative SKR results are provided for Gaussian modulation-based CV-QKD schemes.

In this paper, a semiquantum secret sharing (SQSS) protocol based on x-type states is proposed, which can accomplish the goal that only when two classical communicants cooperate together can they extract the shared secret key of a quantum communicant. Detailed security analysis turns out that this protocol can resist the participant attack and the outside attack. This protocol has some merits: (1) it only requires one kind of quantum entangled state as the initial quantum resource; (2) it doesn't employ quantum entanglement swapping or unitary operations; and (3) it needn't share private keys among different participants beforehand.

The mass migration of rural citizens toward urban areas in search of better employment opportunities, better education erupts a new threat for urban citizens. The increased population due to migration contributes in increasing traffic jams, green house gas emissions, waste disposal. To provide better day‐to‐day services to citizens, common issues such as fair broadband distribution and connectivity, digital and knowledge inclusion needs to be respected with possible integration and smooth management of various social, physical, and business infrastructure. Furthermore, the rapid development of digital society opens up vast of opportunities in smart cities thus implementing goals of education and healthcare for all, green society, green city. However, the continued adoption of new technologies such as internet of things (IoT) and cloud technologies for various applications in smart cities suffers from issues such as high latency, bandwidth bottlenecks, scalability, security, and privacy. The smart cities are usually autonomous in nature, which relies on distributed infrastructure and features applications such as intelligent information processing, heterogeneous network infrastructure, ubiquitous sensing, and intelligent control systems implemented in areas such as public safety, healthcare, and diagnosis. Besides, the blockchain‐enabled applications such as data platform for sharing valuable data between non‐trusted organizations, blockchain‐based financial systems, online games, online education system, and identity management system improve reliability and democratization of cities by eliminating centralization. However, majority of applications depends on either digital signature or public key cryptography‐based schemes which, in turn, depend on the premise that computation of private key from public key is computationally hard. But with advent of quantum computer, the time complexity of all hard problems such as discrete log problem and integer factorization has reduced from millions of years to few seconds, thus endangering traditional cryptographic mechanism, which includes public key, secret key, and digital signature–based protocols used in blockchain technology–based services in smart cities. The quantum computing which uses law of physics for communication does not depend on mathematically hard problems. In addition, convergence of quantum computing with blockchain technology provides us with amicable solutions for smart cities. This chapter discusses overview of quantum computing, key characteristics, and quantum key distribution and presents an architecture enabling post‐quantum blockchain–based applications within smart cities. In addition, the need of various services relying on quantum blockchain in smart cities is presented. Moreover, to enable conceptual architecture for post‐quantum blockchain– enabled services in smart cities, smart contracts are designed for implementing transportation application.

In this paper, we put forward a novel single-state three-party semiquantum key agreement (SQKA) protocol with three-particle GHZ entangled states first. Different with previous quantum key agreement (QKA) protocols, the proposed single-state three-party SQKA protocol can realize the goal that a quantum party and two classical parties who only possess limited quantum capabilities equally contribute to the generation of a shared private key over quantum channels. Detailed security analysis turns out that the proposed single-state three-party SQKA protocol is secure against several famous attacks from an outside eavesdropper, such as the Trojan horse attack, the entangle-measure attack, the measure-resend attack and the intercept-resend attack. Moreover, it can resist the participant attack, which means that the shared private key cannot be determined fully by any nontrivial subset of three parties. The proposed single-state three-party SQKA protocol has the following nice features: (1) it only employs one kind of three-particle GHZ entangled states as initial quantum resource; (2) it does not need pre-shared keys among different parties; (3) it does not need unitary operations or quantum entanglement swapping. Finally, we generalize the proposed single-state three-party SQKA protocol into the case of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document}-party by only employing one kind of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document}-particle GHZ entangled states as initial quantum resource, which inherits the nice features of its three-party counterpart.

Cryptographic key exchange protocols traditionally rely on computational conjectures such as the hardness of prime factorization1 to provide security against eavesdropping attacks. Remarkably, quantum key distribution protocols such as the Bennett–Brassard scheme2 provide information-theoretic security against such attacks, a much stronger form of security unreachable by classical means. However, quantum protocols realized so far are subject to a new class of attacks exploiting a mismatch between the quantum states or measurements implemented and their theoretical modelling, as demonstrated in numerous experiments3–6. Here we present the experimental realization of a complete quantum key distribution protocol immune to these vulnerabilities, following Ekert’s pioneering proposal7 to use entanglement to bound an adversary’s information from Bell’s theorem8. By combining theoretical developments with an improved optical fibre link generating entanglement between two trapped-ion qubits, we obtain 95,628 key bits with device-independent security9–12 from 1.5 million Bell pairs created during eight hours of run time. We take steps to ensure that information on the measurement results is inaccessible to an eavesdropper. These measurements are performed without space-like separation. Our result shows that provably secure cryptography under general assumptions is possible with real-world devices, and paves the way for further quantum information applications based on the device-independence principle. This study demonstrates the experimental realization of a complete protocol for quantum key distribution using entangled trapped strontium ions with device-independent quantum security guarantees.

Quantum key agreement (QKA) permits participants to constitute a shared key on a quantum channel, while no participants can independently determine the shared key. However, existing Measurement-device-independent (MDI) protocols cannot resist channel noise, and noise-resistant QKA protocols cannot resist side-channel attacks caused by equipment defects. In this paper, we design a MDI-QKA protocol against collective-dephasing noise based on GHZ states. First, in our protocol, Alice and Bob prepare a certain number of GHZ states respectively, and then send two particles of each GHZ state to Charlie for bell measurement. Results are that Alice and Bob can obtain Bell states through entanglement exchange with the help of dishonest Charlie. Meanwhile our protocol can ensure the transmission process noise-resisted. Then, Alice and Bob encode their key components to the particle in their hands and construct logical quantum states against collective noise through additional particles and CNOT operation to implement MDI-QKA. Compared with existing MDI-QKA protocols, our protocol uses logical quantum states during particle transmission, which makes the protocol immune to collective-dephasing noise and thus improves the final key rate. Security analysis shows that our protocol can resist common insider and outsider attacks.

The ability to manipulate light at the level of single photons, its elementary excitation quanta, has recently made it possible to produce a rich variety of tailor-made quantum states and arbitrary quantum operations, of high interest for fundamental science and applications. Here we present a concise review of the progress made over the last few decades in the engineering of quantum light states. Although far from exhaustive, this review aims at providing a sufficiently wide and updated introduction that may serve as the entry point to such a fascinating and rapidly evolving field.

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