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The concept of transition in quantum mechanics
Abstract
The concept of quantum transition is critically examined from the perspective of the modern quantum theory of measurement. Historically rooted in the famous quantum jump of the Old Quantum Theory, the transition idea survives today in experimental jargon due to (1) the notion of uncontrollable disturbance of a system by measurement operations and (2) the wave-packet reduction hypothesis in several forms. Explicit counterexamples to both (1) and (2) are presented in terms of quantum measurement theory. It is concluded that the idea of transition, or quantum jump, can no longer be rationally comprehended within the framework of contemporary physical theory.
... Classically, signals are amplified to overcome loss. The same solution is impossible in the quantum case due to the no-cloning theorem [8][9][10], which renders copying arbitrary quantum states impossible. ...
... where ⟨t⟩ is the average value of t over all the test rounds. Finally, we use R and the average value of p s to calculate the success rate according to equation (8). The processing code that realizes this calculation has been made publicly available at [81]. ...
We perform a numerical study of the distribution of entanglement on a real-world fiber grid connecting the German cities of Bonn and Berlin. The connection is realized using a chain of processing-node quantum repeaters spanning roughly 900 kilometers. Their placement is constrained by the fiber grid we consider, resulting in asymmetric links. We investigate how minimal hardware requirements depend on the target application, as well as on the number of repeaters in the chain. We find that requirements for blind quantum computing are markedly different than those for quantum key distribution, with the required coherence time being around two and a half times larger for the former. Further, we observe a trade-off regarding how target secret-key rates are achieved when using different numbers of repeaters: comparatively low-quality entangled states generated at a high rate are preferred for higher numbers of repeaters, whereas comparatively high-quality states generated at a lower rate are favored for lower numbers of repeaters. To obtain our results we employ an extensive simulation framework implemented using NetSquid, a discrete-event simulator for quantum networks. These are combined with an optimization methodology based on genetic algorithms to determine minimal hardware requirements.
... The use of quantum information in DC mitigates the doublespending issue by leveraging the no-cloning principle that prohibits the copy of an arbitrary quantum state [7], [8] . This property is generally useful for all payments and particularly relevant for offline payments where an intermediary may not be available to attest to the truth. ...
... A key advantage of the proposed approach is that all of the properties associated with the quantum representation of money are retained despite the wallet being classical. In a quantum banknote transfer scenario, the physical quantum transfer of the banknote from the payer to the payee (receiver) ensures new and unique ownership of the banknote, a result of the no-cloning principle [7], [8] inherent in quantum information, preventing the payer from retaining a record of the banknote after its transfer to the payee. ...
A digital currency is money in a digital form. In this model, maintaining integrity of the supply is a core concern, therefore protections against double-spending are often at the heart of a secure digital money scheme. Quantum money exploits the quantum mechanical principle of no-cloning to enable a currency that is immune to double spending. One of the challenges of the scheme is that users require technology that is currently out of reach. Here, we propose a model for quantum currency, which alleviates the need for quantum wallets by delegating quantum storage and processing to an intermediary that we call a "quantum vault". We develop the basic building blocks of this quantum-enabled digital currency and discuss its benefits and challenges.
... The collapse of the quantum states leads to an important feature of quantum information. A general quantum state can never be copied or cloned, it can only be transferred [28][29][30]. This is in stark contrast to our experience with classical bits. ...
... The measurement on Alice's side is not only essential for the protocol, it is also important to avoid a contradiction with the no-cloning theorem [28,29]. The no-cloning theorem is a so-called no-go theorem, a proof that shows the impossibility of something. ...
Quantum teleportation is a concept that fascinates and confuses many people, in particular, given that it combines quantum physics and the concept of teleportation. With quantum teleportation likely to play a key role in several communication technologies and the quantum internet in the future, it is imperative to create learning tools and approaches that can accurately and effectively communicate the concept. Recent research has indicated the importance of teachers enthusing students about the topic of quantum physics. Therefore, educators at both high school and early university level need to find engaging and perhaps unorthodox ways of teaching complex, yet interesting topics such as quantum teleportation. In this paper, we present a paradigm to teach the concept of quantum teleportation using the Christmas gift-bringer Santa Claus. Using the example of Santa Claus, we use an unusual context to explore the key aspects of quantum teleportation, and all without being overly abstract. In addition, we outline a worksheet designed for use in the classroom setting which is based on common naive conceptions from quantum physics. This worksheet will be evaluated as a classroom resource to teach quantum teleportation in a subsequent study.
... and quantum measurement cannot be regarded as a cloning process. This is consistent with the well known no-cloning theorem, which forbids cloning in quantum systems [13,14]. ...
... The preceding discussion highlights that classical and quantum information are two distinct types of information. Classical information is clonable, while quantum information is not, as stipulated by the well-known quantum no-cloning theorem [13,14]. A computer that directly processes classical information is a classical computer, while a computer that processes quantum information directly is a quantum computer. ...
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by a basic fact: mathematicians and computers are physical objects subject to the laws of physics. Through an analysis of the Turing machine, it becomes evident that Turing and his contemporaries overlooked a physical possibility: information carriers can be quantum systems. As a result, computing models like the Turing machine can only process classical information, limiting their computing power. Gödel's incompleteness theorem highlights the basic fact that mathematicians and computers are made up of finite numbers of atoms and molecules. They can only start with a finite number of axioms, use a finite number of symbols and deduction rules, and arrive at theorems with a finite number of steps. While the number of proofs may be infinite after including all future mathematicians and computers, they must still be enumerable. In contrast, the number of mathematical statements is uncountable, meaning that there will always be mathematical statements that cannot be proved true or false. Just as Landauer claimed that information is physical, mathematics is also physical, limited or empowered by the physical entities that carries it out or embodies it.
... In the 1960s, Stephen Wiesner introduced conjugate coding [56], laying early groundwork. The 1970s witnessed critical theoretical developments, including James Park's no-cloning theorem [43] and Alexander Holevo's insights [30] into quantum information capacity. By the 1980s, Paul Benioff and David Deutsch expanded on theoretical models, culminating in Deutsch's proposal of the first universal quantum computer in 1985. ...
The dissertation provides a detailed account of our research on developing a quantum algorithm for the Traveling Salesperson Problem (TSP). TSP involves finding the shortest route through a city network, a known NP-hard problem. We introduce a quantum polynomial time algorithm addressing the existence of a Hamiltonian cycle in a graph and the more complex task of determining the shortest Hamiltonian cycle in the context of TSP. Preliminary results suggest our quantum algorithm offers exponential speedup over classical counterparts, albeit with a small probability.
... The information-disturbance principle is closely related to the no-cloning principle[Par70,Die82,WZ82,Ort18] which states that it is, in general, impossible to make a perfect copy of an unknown quantum state. Notably, if one could make such perfect copies, then information on a state could be obtained without disturbing it by making and measuring such a copy. ...
A quantum tamper-evident encryption scheme is a non-interactive symmetric-key encryption scheme mapping classical messages to quantum ciphertexts such that an honest recipient of a ciphertext can detect with high probability any meaningful eavesdropping. This quantum cryptographic primitive was first introduced by Gottesman in 2003. Beyond formally defining this security notion, Gottesman's work had three main contributions: showing that any quantum authentication scheme is also a tamper-evident scheme, noting that a quantum key distribution scheme can be constructed from any tamper-evident scheme, and constructing a prepare-and-measure tamper-evident scheme using only Wiesner states inspired by Shor and Preskill's proof of security for the BB84 quantum key distribution scheme. In this work, we further our understanding of tamper-evident encryption by formally relating it to other cryptographic primitives in an information-theoretic setting. In particular, we show that tamper evidence implies encryption, answering a question left open by Gottesman, we show that it can be constructed from any encryption scheme with revocation and vice-versa, and we formalize an existing sketch of a construction of quantum money from any tamper-evident encryption scheme. These results also yield as a corollary that any scheme allowing the revocation of a message must be an encryption scheme. Finally, we show separations between tamper evidence and other primitives, notably that tamper evidence does not imply authentication and does not imply uncloneable encryption.
... Unclonable cryptography uses the no-cloning principle of quantum mechanics [Par70,WZ82,Die82] to enable cryptographic properties that are impossible to achieve classically. Constructing primitives with such properties has been an active area of research for the past four decades, starting with the well-studied notion of quantum money [Wie83]. ...
We initiate the study of untelegraphable encryption (UTE), founded on the no-telegraphing principle, which allows an encryptor to encrypt a message such that a binary string representation of the ciphertext cannot be decrypted by a user with the secret key, a task that is classically impossible. This is a natural relaxation of unclonable encryption, inspired by the recent work of Nehoran and Zhandry (ITCS 2024), who showed a computational separation between the no-cloning and no-telegraphing principles. In this work, we define and construct UTE information-theoretically in the plain model. Building off this, we give several applications of UTE and study the interplay of UTE with UE and well-studied tasks in quantum state learning, yielding the following contributions: - A construction of collusion-resistant UTE from standard secret-key encryption. We additionally show that hyper-efficient shadow tomography (HEST) is impossible assuming collusion-resistant UTE exists. By considering a relaxation of collusion-resistant UTE, we are able to show the impossibility of HEST assuming only pseudorandom state generators (which may not imply one-way functions). This almost completely answers an open inquiry of Aaronson (STOC 2019). - A construction of UTE from a one-shot message authentication code in the classical oracle model, such that there is an explicit attack that breaks UE security for an unbounded polynomial number of decryptors. - A construction of everlasting secure collusion-resistant UTE, where the decryptor adversary can run in unbounded time, in the quantum random oracle model (QROM), and formal evidence that a construction in the plain model is a challenging task. We additionally show that HEST with unbounded post-processing time is impossible in the QROM. - Constructions (and definitions) of untelegraphable secret sharing and untelegraphable functional encryption.
... The classical inspiration in error correction is exemplified by the repetition code, which produces errorprotected logical units by the replication of bits, as an error on one bit can be corrected by a simple majority vote on the set. Naïvely, this result does not seem translatable to quantum computation, since the no-cloning theorem for qubits precludes the possibility of replicating a qubit's state [Die82;Par70;WZ82]. ...
Quantum computation has long been dominated by a digital approach using the qubit, which exists in a two-dimensional vector space, as its basic unit. More recently, there has been increasing interest in an analog approach, which uses as its basic unit a qudit in an infinite-dimensional vector space. Alongside these two approaches is a third less-studied approach, that of combining digital and analog quantum computation. This approach is perhaps best exemplified by, and most researched via, the system of a qubit coupled to a quantum harmonic oscillator, which has been realized with many of the leading platforms for quantum computation. In this thesis, we ask how machine learning and other high-level computational techniques can be employed in the design of applications of a qubit-oscillator system to implementing fundamental components of quantum technology. In order to begin to answer this question and lay the groundwork for future investigation, both with this system and with others, we demonstrate the application of such high-level computational techniques toward addressing the problems of quantum compilation, quantum sensing, and quantum error-correction with the qubit-oscillator system.
... In quantum mechanics, no-go theorems describe physically impossible situations, impacting quantum computer operations. Examples include the no-cloning [53], no-deleting [54], and no-programming theorems [55], which limit copying, deleting, and perfectly discriminating quantum states [56]. ...
Context: Quantum software development is a complex and intricate process that diverges significantly from traditional software development. Quantum computing and quantum software are deeply entangled with quantum mechanics, which introduces a different level of abstraction and a deep dependence on quantum physical properties. The classical requirements engineering methods must be adapted to encompass the essential quantum features in this new paradigm. Aim: This study aims to systematically identify and analyze challenges, opportunities, developments, and new lines of research in requirements engineering for quantum computing. Method: We conducted a systematic literature review, including three research questions. This study included 105 papers published from 2017 to 2024. Results: The main results include the identification of problems associated with defining specific requirements for quantum software and hybrid system requirements. In addition, we identified challenges related to the absence of standards for quantum requirements engineering. Finally, we can see the advances in developing programming languages and simulation tools for developing software in hybrid systems. Conclusions: This study presents the challenges and opportunities in quantum computing requirements engineering, emphasizing the need for new methodologies and tools. It proposes a roadmap for future research to develop a standardized framework, contributing to theoretical foundations and practical applications.
... Similar notions of -extendibility have been explored for quantum channels [20,25,26]. The unextendibility of a resourceful quantum channel arises from its inability to broadcast the same quantum data to multiple parties and is closely related to the no-cloning theorem [30,31]. Unextendibility has also been studied in some resource-theoretic frameworks [26,32], and it has been used to obtain tight bounds on information processing quantities such as one-way distillable entanglement [33][34][35][36] and distillable secret key [12,14,15]. ...
Quantum communication relies on the existence of high quality quantum channels to exchange information. In practice, however, all communication links are affected by noise from the environment. Here we investigate the ability of quantum channels to perform quantum communication tasks by restricting the participants to use only local operations and one-way classical communication (one-way LOCC) along with the available quantum channel. In particular, a channel can be used to distill a highly entangled state between two parties, which further enables quantum or private communication. In this work, we invoke the framework of superchannels to study the distillation of a resourceful quantum state, such as a maximally entangled state or a private state, using multiple instances of a point-to-point quantum channel. We use the idea of k-extendibility to obtain a semidefinite relaxation of the set of one-way LOCC superchannels and define a class of entanglement measures for quantum channels that decrease monotonically under such superchannels; therefore these measures, dubbed collectively the ``unextendible entanglement of a channel'', yield upper bounds on several communication-theoretic quantities of interest in the regimes of resource distillation and zero error. We then generalize the formalism of k-extendibility to bipartite superchannels, thus obtaining functions that are monotone under two-extendible superchannels. This allows us to analyze probabilistic distillation of ebits or secret key bits from a bipartite state when using a resourceful quantum channel. Moreover, we propose semidefinite programs to evaluate several of these quantities, providing a computationally feasible method of comparison between quantum channels for resource distillation.
... Conversely, one of the most distinctive features of quantum information theory is that quantum states cannot be perfectly cloned. This is a seminal result historically known as the no-cloning theorem [1,2], and a key enabling feature of quantum cryptographic protocols [3]. Indeed, the no-cloning theorem can be used to prove the unconditional security of quantum cryptography protocols, i.e. without relying on computational complexity results or assumptions on the resources available to an eavesdropper as in classical cryptography. ...
A seminal task in quantum information theory is to realize a device able to produce copies of a generic input state with the highest possible output fidelity, thus realizing an \textit{optimal} quantum cloning machine. Recently, the concept of variational quantum cloning was introduced: a quantum machine learning algorithm through which, by exploiting a classical feedback loop informed by the output of a quantum processing unit, the system can self-learn the programming required for an optimal quantum cloning strategy. In this work, we experimentally implement a variational cloning machine of dual-rail encoded photonic qubits, both for phase-covariant and state-dependent cloning. We exploit a fully programmable 6-mode universal integrated device and classical feedback to reach near-optimal cloning performances. Our results demonstrate the potential of programmable integrated photonic platforms for variational self-learning of quantum algorithms.
... On the other hand, the same principles impose constraints on the physical processes [5,6], leading to no-go theorems, which include no-cloning [7][8][9][10], no-broadcasting [11][12][13], and no-deletion theorems [14] (also see [15][16][17]). For instance, the no-cloning theorem [8] prohibits the production of exact copies of an arbitrary quantum state and at the same time, is responsible for detecting eavesdroppers in quantum key distribution (QKD) [3]. ...
The telecloning protocol distributes quantum states from a single sender to multiple receivers via a shared entangled state by exploiting the notions of teleportation and approximate cloning. We investigate the optimal telecloning fidelities obtained using both Gaussian and non-Gaussian shared resources. When the shared non-Gaussian state is created by subtracting photons from both the modes of the Gaussian two-mode squeezed vacuum state, we demonstrate that higher telecloning fidelities can be achieved in comparison with its Gaussian counterpart. To quantify this advantage, we introduce a quadrature-based nonclassicality measure, which is capable of estimating the fidelity of the clones, both with Gaussian and non-Gaussian resource states. We further provide a linear optical setup for asymmetric telecloning of continuous variable states using a multimode entangled state
... In addition, we can not trivially multi-program multiple quantum programs on the same QPU to increase utilization since QPU qubits can interfere with each other in undesirable and unpredictable ways [52], severely degrading performance [47]. Finally, it is generally impossible to save or copy a quantum program during execution [56], which further limits scheduling opportunities for preemption or resource sharing in general. State-of-the-Art of Quantum Software Systems. ...
We introduce the Quantum Operating System (QOS), a unified system stack for managing quantum resources while mitigating their inherent limitations, namely their limited and noisy qubits, (temporal and spatial) heterogeneities, and load imbalance. QOS features the -- a modular and composable compiler for analyzing and optimizing quantum applications to run on small and noisy quantum devices with high performance and configurable overheads. For scalable execution of the optimized applications, we propose the -- an efficient quantum resource management system that multi-programs and schedules the applications across space and time while achieving high system utilization, low waiting times, and high-quality results. We evaluate QOS on real quantum devices hosted by IBM, using 7000 real quantum runs of more than 70.000 benchmark instances. We show that the QOS compiler achieves 2.6--456.5 higher quality results, while the QOS runtime further improves the quality by 1.15--9.6 and reduces the waiting times by up to 5 while sacrificing only 1--3\% of results quality (or fidelity).
... Quantum networks utilize light as the primary information carrier between nodes of the network. Unlike their clas-sical counterparts, arbitrary quantum states cannot be copied faithfully [24]- [26], making classical signal amplification schemes impossible to apply [27]. Furthermore, as quantum nodes exchange information via single photons, attenuation becomes a major obstacle to scaling of quantum networks. ...
Quantum networks are expected to enhance distributed quantum computing and quantum communication over long distances while providing security dependent upon physical effects rather than mathematical assumptions. Through simulation, we show that a quantum network utilizing only entanglement purification or only quantum error correction as error management strategies cannot create Bell pairs with fidelity that exceeds the requirement for a secured quantum key distribution protocol for a broad range of hardware parameters. We propose hybrid strategies utilizing quantum error correction on top of purification and show that they can produce Bell pairs of sufficiently high fidelity. We identify the error parameter regime for gate and measurement errors in which these hybrid strategies are applicable.
... The presented approach remains correct if, e.g., |ψ d is a three-qubit state and |ψ c is a two-qubit state. However, the laws of quantum mechanics, like non-cloning (Park, 1970;Wootters and Zurek, 1982;Ortigoso, 2018) and no-deleting (Pati and Braunstein, 2000) theorems impose the same number of qubits on the circuit's input and output, unlike, for example, in classical neural networks. ...
... The loss of photons in quantum networking is critical because, unlike in classical networking, we cannot copy quantum data for backup due to the no-cloning theorem [16], [17]. Since we can repeat attempts to create entanglement but cannot afford to lose critical quantum data, the consensus approach today is to build applications on top of quantum network architectures that provide end-to-end entanglement generation as the fundamental service [18]. ...
... The loss of photons in quantum networking is critical because, unlike in classical networking, we cannot copy quantum data for backup due to the no-cloning theorem [16], [17]. Since we can repeat attempts to create entanglement but cannot afford to lose critical quantum data, the consensus approach today is to build applications on top of quantum network architectures that provide end-to-end entanglement generation as the fundamental service [18]. ...
... However, generating entanglement over a long distance or even in a complex, large-scale data center network is difficult due to inherent fiber attenuation. In classical communication, it is conventional to copy and resend the data in the middle of a link with the help of repeaters, but for the quantum case, we cannot use the same approach due to the no-cloning theorem [12], [13]. One promising method for entanglement distribution is generating link-level Bell pairs and utilizing quantum repeaters to perform entanglement swapping [14] and entanglement purification [15], expanding a set of linklevel entanglement shared between two adjacent nodes into a long-length distributed entanglement. ...
The heterogeneity of quantum link architectures is an essential theme in designing quantum networks for technological interoperability and possibly performance optimization. However, the performance of heterogeneously connected quantum links has not yet been addressed. Here, we investigate the integration of two inherently different technologies, with one link where the photons flow from the nodes toward a device in the middle of the link, and a different link where pairs of photons flow from a device in the middle towards the nodes. We utilize the quantum internet simulator QuISP to conduct simulations. We first optimize the existing photon pair protocol for a single link by taking the pulse rate into account. Here, we find that increasing the pulse rate can actually decrease the overall performance. Using our optimized links, we demonstrate that heterogeneous networks actually work. Their performance is highly dependent on link configuration, but we observe no significant decrease in generation rate compared to homogeneous networks. This work provides insights into the phenomena we likely will observe when introducing technological heterogeneity into quantum networks, which is crucial for creating a scalable and robust quantum internetwork.
... The loss of photons in quantum networking is critical because, unlike in classical networking, we cannot copy quantum data for backup due to the no-cloning theorem [16], [17]. Since we can repeat attempts to create entanglement but cannot afford to lose critical quantum data, the consensus approach today is to build applications on top of quantum network architectures that provide end-to-end entanglement generation as the fundamental service [18]. ...
The optical Bell State Analyzer (BSA) plays a key role in the optical generation of entanglement in quantum networks. The optical BSA is effective in controlling the timing of arriving photons to achieve interference. It is unclear whether timing synchronization is possible even in multi-hop and complex large-scale networks, and if so, how efficient it is. We investigate the scalability of BSA synchronization mechanisms over multiple hops for quantum networks both with and without memory in each node. We first focus on the exchange of entanglement between two network nodes via a BSA, especially effective methods of optical path coordination in achieving the simultaneous arrival of photons at the BSA. In optical memoryless quantum networks, including repeater graph state networks, we see that the quantum optical path coordination works well, though some possible timing coordination mechanisms have effects that cascade to adjacent links and beyond, some of which was not going to work well of timing coordination. We also discuss the effect of quantum memory, given that end-to-end extension of entangled states through multi-node entanglement exchange is essential for the practical application of quantum networks. Finally, cycles of all-optical links in the network topology are shown to may not be to synchronize, this property should be taken into account when considering synchronization in large networks.
... Quantum networks are essential for distributed quantum computing, relying on the exchange of quantum states among different devices. Unlike conventional networks, quantum networks face the challenge of the no-cloning theorem, which prohibits copying arbitrary quantum states [44]. To overcome this limitation, quantum networks utilize entanglement and quantum teleportation. ...
... There is a glaring contradiction, duly noted in [1], between ubiquity of transmission of classical information in everyday life, and multitude of no-go theorems, such as no-cloning [2,3,4], noteleportation [5], no-broadcasting [6], no-communication [7], no-signaling [8], which disallow information, contained in arbitrary state, from being copied. The unfeasibility could be ascertained multiple ways: ...
I reveal the underlying mechanism of information transmission.
... Before the inception of QC and QI in the 1970s, the race to design the smallest integrated circuits and build the most powerful supercomputers was based on a classical model of computing, where binary logic is the underlying language. After the seminal work of Feynman and others [1][2][3][4][5][6][7], quantum computers have introduced a new language of computing based on quantum mechanics (QM), providing us with a totally novel way of simulating new problems and designing new algorithms with the ultimate goal of performing certain tasks faster than their classical counterparts. ...
This pedagogical article elucidates the fundamentals of trapped-ion quantum computing, which is one of the potential platforms for constructing a scalable quantum computer. The evaluation of a trapped-ion system's viability for quantum computing is conducted in accordance with DiVincenzo's criteria.
... Correct routing of the signals from their source to the destination is essential in a network for both classical and quantum communications [15]. The impossibility of perfect cloning [16,17] prevents multi-directional broadcast in a quantum network. Therefore, quantum routing needs advanced mechanisms. ...
In quantum communication, the perfect state transfer (PST) is a crucial tool for transferring information. But it is not readily applicable to communicate between any pair of vertices in an arbitrary network. In this article, we consider a spin–spin interaction network governed by XX+YY Hamiltonian. We design a quantum routing protocol based on PST with single-excitation state of the system Hamiltonian to overcome this challenge. The vertices and edges of the network represent the qubits and their interactions, respectively. We take the privilege to switch on or off any interaction, that assists us to perform multiple perfect state transfers in a graph simultaneously. We also build up a salable network allowing quantum communication between two arbitrary vertices. Later, we utilize the combinatorial characteristics of hypercube graphs to propose a static routing schema to communicate simultaneously between a set of senders and a set of receivers in a planar network. Our construction is new and significantly powerful. We illustrate multiple examples of planar graphs supporting quantum routing where classical routing is impossible.
... Permutation symmetry in the extension of a bipartite quantum state indicates a lack of entanglement in that state [5,6,7]. This permutation symmetry limits entanglement, which relates to fundamental principles of quantum information like the no-cloning theorem [8,9,10] and entanglement monogamy [11]. Additionally, the lack of a shared reference frame between two parties implies that a quantum state prepared relative to another party's reference frame respects a certain symmetry and is less useful than one breaking that symmetry [12]. ...
Symmetry is a unifying concept in physics. In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks. For example, states that commute with a Hamiltonian realizing a time evolution are not useful for timekeeping during that evolution, and bipartite states that are highly extendible are not strongly entangled and thus not useful for basic tasks like teleportation. Motivated by this perspective, this paper details several quantum algorithms that test the symmetry of quantum states and channels. For the case of testing Bose symmetry of a state, we show that there is a simple and efficient quantum algorithm, while the tests for other kinds of symmetry rely on the aid of a quantum prover. We prove that the acceptance probability of each algorithm is equal to the maximum symmetric fidelity of the state being tested, thus giving a firm operational meaning to these latter resource quantifiers. Special cases of the algorithms test for incoherence or separability of quantum states. We evaluate the performance of these algorithms on choice examples by using the variational approach to quantum algorithms, replacing the quantum prover with a parameterized circuit. We demonstrate this approach for numerous examples using the IBM quantum noiseless and noisy simulators, and we observe that the algorithms perform well in the noiseless case and exhibit noise resilience in the noisy case. We also show that the maximum symmetric fidelities can be calculated by semi-definite programs, which is useful for benchmarking the performance of these algorithms for sufficiently small examples. Finally, we establish various generalizations of the resource theory of asymmetry, with the upshot being that the acceptance probabilities of the algorithms are resource monotones and thus well motivated from the resource-theoretic perspective.
The famous no-cloning principle has been shown recently to enable a number of uncloneable cryptographic primitives, including the copy-protection of certain functionalities. Here we address for the first time unkeyed quantum uncloneablity, via the study of a complexity-theoretic tool that enables a computation, but that is natively unkeyed: quantum advice. Remarkably, this is an application of the no-cloning principle in a context where the quantum states of interest are not chosen by a random process. We establish unconditional constructions for promise problems admitting uncloneable quantum advice and, assuming the feasibility of quantum copy-protecting certain functions, for languages with uncloneable advice. Along the way, we note that state complexity classes, introduced by Rosenthal and Yuen (ITCS 2022) — which concern the computational difficulty of synthesizing sequences of quantum states — can be naturally generalized to obtain state cloning complexity classes. We make initial observations on these classes, notably obtaining a result analogous to the existence of undecidable problems.
Our proof technique defines and constructs ingenerable sequences of finite bit strings, essentially meaning that they cannot be generated by any uniform circuit family with non-negligible probability. We then prove a generic result showing that the difficulty of accomplishing a computational task on uniformly random inputs implies its difficulty on any fixed, ingenerable sequence. We use this result to derandomize quantum cryptographic games that relate to cloning, and then incorporate a result of Kundu and Tan (arXiv 2022) to obtain uncloneable advice. Applying this two-step process to a monogamy-of-entanglement game yields a promise problem with uncloneable advice, and applying it to the quantum copy-protection of pseudorandom functions with super-logarithmic output lengths yields a language with uncloneable advice.
Every new generation of mobile networks brings significant advances in two segments, enhancement of the network parameters within the legacy technologies and introduction of new technologies enabling new paradigms in designing the networks. In the first class of enhancements the effort is to increase data rates, improve energy efficiency, enhance connectivity, reduce data transmission latency etc. In the second class of innovations for 6G and 7G, we anticipate focus on optimum integration of advanced ML and AI in general, and quantum computing with the continuous interest in the satellite networks for optimal quantum key distribution . By introducing quantum technology 7G will be able to speed up computing processes in the net, enhance network security as well as to enable distributed QC, which is a new paradigm in computer sciences. Using advanced networks as a basic ingredient of inter system integration, here we focus only on the second segment of anticipated innovations in networking and present a survey of the subset of potential technology enablers for the above concept with special emphasis on the inter dependency of the solutions chosen in different segments of the network. In Section II, we present several anticipated 6G/7G (system of systems type) network optimization examples resulting in a new paradigm of network optimization indicating a need for quantum computing and quantum computing based optimization algorithms. In Section III we survey work on quantum cryptography and QKD.
Following Einstein’s prediction that “Physics constitutes a logical system of thought” and “Nature is the realization of the simplest conceivable mathematical ideas”, this topical review outlines a formal extension of local realism limited by the speed of light to global realism with bipolar strings (GRBS) that unifies the principle of locality with quantum nonlocality. The related literature is critically reviewed to justify GRBS which is shown as a necessary and inevitable consequence of the Bell test and an equilibrium-based axiomatization of physics and quantum information science for brain–universe similarity and human-level intelligence. With definable causality in regularity and mind–light–matter unity for quantum superposition/entanglement, bipolar universal modus ponens (BUMP) in GRBS makes quantum emergence and submergence of spacetime logically ubiquitous in both the physical and mental worlds—an unexpected but long-sought simplification of quantum gravity with complete background independence. It is shown that GRBS forms a basis for quantum intelligence (QI)—a spacetime transcendent, quantum–digital compatible, analytical quantum computing paradigm where bipolar strings lead to bipolar entropy as a nonlinear bipolar dynamic and set–theoretic unification of order and disorder as well as linearity and nonlinearity for energy/information conservation, regeneration, and degeneration toward quantum cognition and quantum biology (QCQB) as well as information-conservational blackhole keypad compression and big bang data recovery. Subsequently, GRBS is justified as a real-world quantum gravity (RWQG) theory—a bipolar relativistic causal–logical reconceptualization and unification of string theory, loop quantum gravity, and M-theory—the three roads to quantum gravity. Based on GRBS, the following is posited: (1) life is a living bipolar superstring regulated by bipolar entropy; (2) thinking with consciousness and memory growth as a prerequisite for human-level intelligence is fundamentally mind–light–matter unitary QI logically equivalent to quantum emergence (entanglement) and submergence (collapse) of spacetime. These two posits lead to a positive answer to the question “If AI machine cannot think, can QI machine think?”. Causal–logical brain modeling (CLBM) for entangled machine thinking and imagination (EMTI) is proposed and graphically illustrated. The testability and falsifiability of GRBS are discussed.
Catalysts open up new reaction pathways that can speed up chemical reactions while not consuming the catalyst. A similar phenomenon has been discovered in quantum information science, where physical transformations become possible by utilizing a quantum degree of freedom that returns to its initial state at the end of the process. In this review, a comprehensive overview of the concept of catalysis in quantum information science is presented and its applications in various physical contexts are discussed.
Ethereum's current Gasper consensus mechanism, which combines the Latest Message Driven Greediest Heaviest Observed SubTree (LMD-GHOST) fork choice rule with the probabilistic Casper the Friendly Finality Gadget (FFG) finality overlay, finalizes transactions in 64 to 95 blocks, an approximate 15-minute delay. This finalization latency impacts user experience and exposes the network to short-term chain reorganization risks, potentially enabling transaction censorship or frontrunning by validators without severe penalties. As the ecosystem pursues a rollup-centric roadmap to scale Ethereum into a secure global settlement layer, faster finality allows cross-layer and inter-rollup communication with greater immediacy, reducing capital inefficiencies. Single slot finality (SSF), wherein transactions are finalized within the same slot they are proposed, promises to advance the Ethereum protocol and enable better user experiences by enabling near-instant economic finality. This thesis systematically studies distributed consensus protocols through propose-vote-merge, PBFT-inspired, and graded agreement families - scrutinizing their capacities to enhance or replace LMD-GHOST. The analysis delves into the intricate tradeoffs between safety, liveness, and finality, shedding light on the challenges and opportunities in designing an optimal consensus protocol for Ethereum. It also explores different design decisions and mechanisms by which single slot or fast finality can be enabled, including cumulative finality, subsampling, and application-layer fast finality. Furthermore, this work introduces SSF-enabled and streamlined fast finality constructions based on a single-vote total order broadcast protocol. The insights and recommendations in this thesis provide a solid foundation for the Ethereum community to make informed decisions regarding the future direction of the protocol's consensus.
This chapter examines the state-of-the-art field of quantum computing and its significant consequences for digital resilience. Further, it explains the basic ideas behind quantum superposition, entanglement, and the no-cloning theorem, which are necessary to fully understand quantum computing. Along with that, it describes how quantum computing has changed over time, how it differs from classical computing, and how it has dealt with its own problems. It also involves the preliminary study of qubits, quantum gates, and quantum algorithms, exploring the complex field of quantum cryptography and highlighting the importance of quantum key distribution. It also provides additional clarification on quantum applications, such as quantum machine learning and computational chemistry, while discussing problems in error correction, ethical considerations, and potential threats to traditional cryptography. It concludes by remarking on the need to take proactive steps to strengthen and adopt strategies necessary for digital resilience in the upcoming quantum age.
In this study, an effect that we will call entanglement closed loop (ECL) and that results from the implementation of entangled states through quantum Fourier transform (QFT) blocks, is presented. The dual-channel Bell test can be implemented using two linear polarizers (LP) or two half-wave plates (HWP). ECL allows us to verify that the arbitrary relocation of both the LPs and the HWPs is indifferent when it comes to reproducing the results of quantum mechanics. Implementations of two conspicuous relocations of the LPs on an optical table experimentally prove the existence of the entanglement closed loop. Finally, a new interpretation of quantum mechanics based on ECL, which explains the operation of a new family of quantum communications protocols, is presented.
Quantum Data Networks (QDNs) are vital to building Distributed Quantum Computing (DQC) systems. Though several communication protocols have been proposed for QDNs, most of them are at the network layer or below. The only transport layer protocol [1] used batch processing of requests for End-to-End (E2E) quantum data transmission. It not only limits the quantum resource utilization, more importantly, it cannot guarantee reliable E2E quantum data transmission. In this paper, we propose the first asynchronous transportation layer protocol, called AQTP, for QDNs to achieve high-speed and reliable E2E quantum data transmission. AQTP has several distinct features: (i) each quantum node locally allocates quantum resources in order to improve scalability; (ii) requests are processed in an asynchronous manner, which results in a higher quantum resource utilization; and (iii) it ensures reliable data transmission even if the teleportation operations fail. Extensive simulations show that compared with a batch processed transport layer protocol, AQTP can increase the network throughput by up to 82.97%, and reduce the Average Task Completion Time (ATCT) of DQC tasks by up to 94.69%.
Quantum entanglement enables important computing applications such as quantum key distribution. Based on quantum entanglement, quantum networks are built to provide long-distance secret sharing between two remote communication parties. Establishing a multi-hop quantum entanglement exhibits a high failure rate, and existing quantum networks rely on trusted repeater nodes to transmit quantum bits. However, when the scale of a quantum network increases, it requires end-to-end multi-hop quantum entanglements in order to deliver secret bits without letting the repeaters know the secret bits. This work focuses on the entanglement routing problem, whose objective is to build long-distance entanglements via untrusted repeaters for concurrent source-destination pairs through multiple hops. Different from existing work that analyzes the traditional routing techniques on special network topologies, we present a comprehensive entanglement routing model that reflects the differences between quantum networks and classical networks as well as a new entanglement routing algorithm that utilizes the unique properties of quantum networks. Evaluation results show that the proposed algorithm Q-CAST increases the number of successful long-distance entanglements by a big margin compared to other methods. The model and simulator developed by this work may encourage more network researchers to study the entanglement routing problem.
A recent theoretical proposal for teleamplification requires preparation of Fock states, programmable interferometers, and photon-number resolving detectors to herald the teleamplification of an input state. These enable teleportation and heralded noiseless linear amplification of a photonic state up to an arbitrarily large energy cutoff. We report on adapting this proposal for the Borealis boson-sampling device and demonstrating teleamplification of squeezed-vacuum states with variable amplification factors. The results match the theoretical predictions and exhibit features of amplification in the teleported mode, with fidelities from 50 to 93%. This demonstration motivates the continued development of photonic quantum computing hardware for noiseless linear amplification's applications across quantum communication, sensing, and error correction.
The no-cloning theorem asserts that, unlike classical information, quantum information cannot be copied. This seemingly undesirable phenomenon is harnessed in quantum cryptography. Uncloneable cryptography studies settings in which the impossibility of copying is a desired property, and achieves forms of security that are classically unattainable. The first example discovered and analyzed was in the context of cash. On the one hand, we want users to hold the cash; on the other hand, the cash should be hard to counterfeit. Quantum money uses variants of the no-cloning theorem to make counterfeiting impossible.
In the past decade, this field developed in various directions: several flavors of quantum money, such as classically verifiable, locally verifiable, semi-quantum, quantum coins, and quantum lightning were constructed. New uncloneable primitives were introduced, such as uncloneable signatures, quantum copy protection for classical software, pseudorandom states, and several uncloneable forms of encryption. This work is a gentle introduction to these topics.
Sharing entanglement across quantum interconnects is fundamental for quantum information processing. We discuss a practical setting where this interconnect, modeled by a quantum channel, is used once with the aim of sharing high-fidelity entanglement. For any channel, we provide methods to easily find both this maximum fidelity and optimal inputs that achieve it. Unlike most metrics for sharing entanglement, this maximum fidelity can be shown to be multiplicative. This ensures a complete understanding in the sense that the maximum fidelity and optimal inputs found in our one-shot setting extend even when the channel is used multiple times, possibly with other channels. Optimal inputs need not be fully entangled. We find that the minimum entanglement in these optimal inputs can even vary discontinuously with channel noise. Generally, noise parameters are hard to identify and remain unknown for most channels. However, for all qubit channels with qubit environments, we provide a rigorous noise parametrization, which we explain in terms of no cloning. This noise parametrization and a channel representation that we call the standard Kraus decomposition have pleasing properties that make them useful more generally.
The famous no-cloning principle has been shown recently to enable a number of uncloneable functionalities. Here we address for the first time unkeyed quantum uncloneablity, via the study of a complexity-theoretic tool that enables a computation, but that is natively unkeyed: quantum advice. Remarkably, this is an application of the no-cloning principle in a context where the quantum states of interest are not chosen by a random process. We show the unconditional existence of promise problems admitting uncloneable quantum advice, and the existence of languages with uncloneable advice, assuming the feasibility of quantum copy-protecting certain functions. Along the way, we note that state complexity classes, introduced by Rosenthal and Yuen (ITCS 2022) - which concern the computational difficulty of synthesizing sequences of quantum states - can be naturally generalized to obtain state cloning complexity classes. We make initial observations on these classes, notably obtaining a result analogous to the existence of undecidable problems. Our proof technique establishes the existence of ingenerable sequences of finite bit strings - essentially meaning that they cannot be generated by any uniform circuit family. We then prove a generic result showing that the difficulty of accomplishing a computational task on uniformly random inputs implies its difficulty on any fixed, ingenerable sequence. We use this result to derandomize quantum cryptographic games that relate to cloning, and then incorporate a result of Kundu and Tan (arXiv 2022) to obtain uncloneable advice. Applying this two-step process to a monogamy-of-entanglement game yields a promise problem with uncloneable advice, and applying it to the quantum copy-protection of pseudorandom functions with super-logarithmic output lengths yields a language with uncloneable advice.
Quantum theoretical study of interaction between object and apparatus to obtain information in initial state of object from data on resulting state of apparatus; precise mathematical chacterization given for general types of interactions; discussion of L. Landau, J. von Neumann measurements; commentary on L. Durnad's theory of measurement.
A unitary operator is defined, connecting the states of the measured system and the measuring-instrument system before and after interaction, by means of which the post-interaction values of S in the instrument can be used to calculate the pre-interaction 〈R〉av and Δ2R in the measured system, where R and S are Hermitian operators. The premeasurement state of the instrument need not be known, and the same measurement operator is applicable whether the system to be measured is originally described by a pure case or a mixture. Finally, this theory is contrasted briefly with the measurement theory of von Neumann.
The overall purpose of this paper is to clarify the physical meaning and epistemological status of the term 'measurement' as used in quantum theory. After a review of the essential logical structure of quantum physics, Part I presents interpretive discussions contrasting the quantal concepts observable and ensemble with their classical ancestors along the lines of Margenau's latency theory. Against this background various popular ideas concerning the nature of quantum measurement are critically surveyed. The analysis reveals that, in addition to internal mathematical difficulties, all the so-called quantum theories of measurement are grounded in unjustifiable, classical presuppositions.
Recent discussions in the physical literature, designed to clarify the logical position of modern physical theory, have brought to light an amazing divergence of fundamental attitudes which may well bewilder the careful student of physics as well as philosophy. Quantum mechanics, representing an abstract formalism, should be capable of having its logical structure analyzed with great precision like any other mathematical discipline. Its consequences in all problems to which its method can be applied are so unambiguous, consistent, and successful in predicting physical experience as to disperse immediately all thoughts of possible discrepancies in its fundamental texture. Yet it must be said that even the founders of quantum theory are not in harmony in their various expositions of the bases of that theory. However, while this situation seems disquieting on the face of it, there is no cause for serious brow raising, for it is a fact that there exists agreement with regard to the central axioms of the theory, and that the ambiguities affect only their philosophical interpretation, a field in which differences of opinion may at present be honestly entertained.
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We use the term ‘measurement’ to refer to the interaction between an object and an apparatus on the basis of which information concerning the initial state of the object may be obtained from information on the resulting state of the apparatus. The quantum theory of measurement is a quantum theoretic investigation of such interactions in order to analyse the correlations between object and apparatus that measurement must establish. Although there is a sizeable literature on quantum measurements there appear to be just two sorts of interactions that have been employed. There are the ‘disturbing’ interactions consistent with the analysis of Landau and Peierls (8) as developed by Pauli (11) and by Landau and Lifshitz (7), and there are the ‘non-disturbing’ interactions explicitly set out by von Neumann ((10), chs. 5, 6), and that dominate the literature. In this paper we shall investigate the most general types of interactions that could possibly constitute measurements and provide a precise mathematical characterization (section 2). We shall then examine an interesting subclass, corresponding to Landau's ideas, that contains both of the above sorts of measurements (section 3). Finally, we shall discuss von Neumann measurements explicitly and explore the purported limitations suggested by Wigner(12) and Araki and Yanase (2). We hope, in this way, to provide a comprehensive basis for discussions of quantum measurements.(Received December 13 1966)
This paper presents a study of what is sometimes regarded as the conceptual heart of quantum theory, namely, the orthodox physical interpretation of non-commuting operators as representatives of incompatible (non-simultaneously-measurable) observables. To provide a firm foundation for the analysis, a definite statement of the essentials of modern quantum theory is given briefly in the form of a mathematical axiomatization together with a review of the two measurement constructs introduced elsewhere (Park, 1967b). Contrary to custom in discussions on simultaneous measurability, the uncertainty principle is not dwelt upon but simply stated carefully in order to establish its actual irrelevance to the problem at hand. It is then demonstrated that the much quoted principle of incompatibility of noncommuting observables is false. The axiomatic root of all incompatibility arguments is next identified; and it is shown that, with a slight modification of the basic postulates which affects neither useful theorems nor practical calculations, quantum physics no longer entails illogical restrictions on measurability. Among the related topics touched upon are the problem of joint probability distributions, the logical approach to quantum mathematics (wherein noncommutativity becomes incompatibility within a propositional calculus), and the field theoretic attempt to unify quantal and relativistic physics through a postulated connection between incompatibility and space-like intervals.
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