Artur Ekert

University of Oxford | OX · Mathematical Institute

The usual representation of quantum algorithms is limited to the process of solving the problem. We extend it to the process of setting the problem. Bob, the problem setter, selects a problem-setting by the initial measurement. Alice, the problem solver, unitarily computes the corresponding solution and reads it by the final measurement. This simpl...

Sir Peter Knight is a pioneer in quantum optics which has now grown to an important branch of modern physics to study the foundations and applications of quantum physics. He is leading an effort to develop new technologies from quantum mechanics. In this collection of essays, we recall the time we were working with him as a postdoc or a PhD student...

In the 1960s, Landauer argued that information must obey physical principles. What if information follows the rules of quantum mechanics? Feynman first proposed we could use a quantum system to simulate quantum mechanics exponentially faster. Deutsch later proved that the quantum computer is inherently more powerful. The field took off in 1994 afte...

Among those who make a living from the science of secrecy, worry and paranoia are just signs of professionalism. Can we protect our secrets against those who wield superior technological powers? Can we trust those who provide us with tools for protection? Can we even trust ourselves, our own freedom of choice? Recent developments in quantum cryptog...

I always found it an interesting coincidence that the two basic ingredients of modern quantum theory, namely probability and complex numbers, were discovered by the same person, an extraordinary man of many talents, a gambling scholar by the name of Girolamo Cardano. © Springer International Publishing Switzerland 2014. All rights are reserved.

We address the problem of assessing the coherent character of physical evolution. We take the quantum Zeno effect (QZE) as a characteristic trait of quantum dynamics, and derive relations among transfer rates as a function of the strength of a measurement. These relations support the intuition that only quantum dynamics is susceptible to QZE. With...

It is shown that energy transfer in a homogeneous fully connected quantum network is assisted by a decohering interaction with environmental spins. Analytic expressions for the transfer probabilities are obtained for the zero temperature case, and the effect is shown to persist at physiological temperatures. This model of decoherence-assisted energ...

One of the assumptions of Bell's Theorem is the existence of experimental free will, meaning that measurement settings can be chosen perfectly at random. With the advent of quantum information, the violation of a Bell inequality constitutes evidence of the lack of an eavesdropper in cryptographic scenarios such as key distribution and randomness ex...

With the advent of quantum information, the violation of a Bell inequality is used to witness the absence of an eavesdropper in cryptographic scenarios such as key distribution and randomness expansion. One of the key assumptions of Bell's theorem is the existence of experimental "free will," meaning that measurement settings can be chosen at rando...

Once viewed as imposing absolute limits on knowledge and technology, quantum theory is now expanding the power of computers and the vistas of the mind

The concept of nonlocality, whereby a local operation on one state can instantaneously affect the properties of another spatially-separated state, has been investigated through the violation of Bell inequalities. Realisations of such violations in the laboratory paved the way for not only experimental justification of quantum theory, but also one o...

Alan Turing has certainly contributed to a widespread belief that the quest for a perfect, unbreakable, cipher is a futile pursuit. The ancient art of concealing information has, in the past, been matched by the ingenuity of code-breakers, but no longer! With the advent of quantum cryptography, the hopes of would-be eavesdroppers have been dashed,...

Human desire to communicate secretly is at least as old as writing itself and goes back to the beginnings of our civilisation. Over the centuries many ingenious methods of secret communication have been developed, only to be matched by the ingenuity of code-breakers. As a result, the quest for a perfect, unbreakable, cipher, had been declared a fut...

In the absence of errors, the dynamics of a spin chain, with a suitably engineered local Hamiltonian, allow the perfect, coherent transfer of a quantum state over large distances. Here, we propose encoding and decoding procedures to recover perfectly from low rates of systematic errors. The encoding and decoding regions, located at opposite ends of...

With the advent of quantum information, the violation of a Bell inequality is used as evidence of the absence of an eavesdropper in cryptographic scenarios such as key distribution and randomness expansion. One of the key assumptions of Bell's Theorem is the existence of experimental "free will", meaning that measurement settings can be chosen at r...

The dynamics of a dimer coupled to two different environments, each in a spin star configuration under the influence of decoherence, is studied. The exact analytical expression for the transition probability in the dimer system is obtained for different situations, i.e., independent and correlated environments. In all cases considered, it is shown...

The theory of classical universal computation was laid down in 1936, was implemented within a decade, became commercial within another decade, and dominated the world's economy half a century later. This success story relied on the progress in technology. As computers become faster they must become smaller. The history of computer technology has in...

The need for increased memory space and higher speed in computers has fueled the demand for smaller and faster computers. However, as the computer chips miniaturize, it becomes inevitable that we need to look at the possibility of manipulating and addressing atoms and molecules individually. One such possibility is a feasibility study of a quantum...

On the atomic scale, matter obeys the rules of quantum mechanics which are quite different from the classical rules that determine the properties of conventional computers. Today's advanced lithographic techniques can etch logic gates and wires less than a micron across onto the surfaces of silicon chips. Soon they will yield even smaller parts and...

We introduce an algorithm to perform an optimal adiabatic evolution that operates without an apriori knowledge of the system spectrum. By probing the system gap locally, the algorithm maximizes the evolution speed, thus minimizing the total evolution time. We test the algorithm on the Landau-Zener transition and then apply it on the quantum adiabat...

Bell's inequality makes a seemingly insane scenario possible --- devices of unknown or dubious provenance, even those that are manufactured by our enemies, can be safely used for secret communication. And this is for real! All that is needed to implement such a bizarre form of cryptography is a loophole-free violation of Bell's inequalities. It is...

The processes of energy and information transfer in quantum networks play an important role for quantum communication and quantum computation. Unavoidable interaction of the quantum system with the environment leads to decoherence and dissipation, processes typically associated with a destruction of quantum coherence in the system. However, recentl...

In recent years, there has been much synergy between the exciting areas of quantum information science and ultracold atoms. This volume, as part of the proceedings for the XCI session of Les Houches School of Physics (held for the first time outside Europe in Singapore) brings together experts in both fields. The theme of the school focused on two...

Girolamo Cardano was an experienced card player, but that night he was losing money at an alarming rate. No wonder, for he was being cheated. When he realized that the cards were marked, he drew his dagger and stabbed the cheat in the face. Cardano then forced his way out of the gambling den into the narrow streets of Venice, recovering his money o...

This purely recreational paper is about one of the most colorful characters of the Italian Renaissance, Girolamo Cardano, and the discovery of two basic ingredients of quantum theory, probability and complex numbers. The paper is dedicated to Giuseppe Castagnoli on the occasion of his 65th birthday. Back in the early 1990s, Giuseppe instigated a se...

1 Qubits, gates and networks Consider the two binary strings, 011, (1.1) 111. (1.2) The first one can represent, for example, the number 3 (in binary) and the second one the number 7. In general three physical bits can be prepared in 23 = 8 different configurations that can represent, for example, the integers from 0 to 7. However, a register compo...

We address the problem of estimating the phase phi given N copies of the phase rotation u(phi) within an array of quantum operations in finite dimensions. We first consider the special case where the array consists of an arbitrary input state followed by any arrangement of the N phase rotations, and ending with a POVM. We optimise the POVM for a gi...

Assume that two distant parties, Alice and Bob, as well as an adversary, Eve, have access to (quantum) systems prepared jointly according to a tripartite state ρ ABE . In addition, Alice and Bob can use local operations and authenticated public classical communication. Their goal is to establish a key which is unknown to Eve. We initiate the study...

We address the problem of estimating the phase phi given N copies of the phase rotation gate u(phi). We consider, for the first time, the optimization of the general case where the circuit consists of an arbitrary input state, followed by any arrangement of the N phase rotations interspersed with arbitrary quantum operations, and ending with a POVM...

Quantum state transfer through a spin chain via adiabatic dark passage is proposed. This technique is robust against control field fluctuations and unwanted environmental coupling of intermediate spins. Our method can be applied to spin chains with more than three spins. We also propose single qubit rotation using this technique.

We analyse the information obtained by an eavesdropper during the various stages of a quantum cryptographic protocol associated with key distribution . We provide both an upper and a lower limit on the amount of information that may have leaked to the eavesdropper at the end of the key distribution procedure . These limits are restricted to interce...

We examine the decay of two correlated atoms to a reservoir prepared in its ground state and in a squeezed multimode vacuum state. We calculate the entropies for the atoms and use the index of correlation to show the decay and regeneration of correlations between the atoms as they interact with the reservoir.

Quantum computers which use quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations can be viewed as multiparticle interferometers. I discuss this approach to quantum computation and argue that it provides additional insights into the nature of quantum algorithms.

DOI:https://doi.org/10.1103/PhysRevA.74.049907

Assume that two distant parties, Alice and Bob, as well as an adversary, Eve, have access to (quantum) systems prepared jointly according to a tripartite state. In addition, Alice and Bob can use local operations and authenticated public classical communication. Their goal is to establish a key which is unknown to Eve. We initiate the study of this...

Nonlinear properties of quantum states, such as entropy or entanglement, quantify important physical resources and are frequently used in quantum-information science. They are usually calculated from a full description of a quantum state, even though they depend only on a small number of parameters that specify the state. Here we extract a nonlocal...

Introduction Computation is an operation on symbols. We tend to perceive symbols as abstract entities, such as numbers or letters from a given alphabet. However, symbols are always represented by selected properties of physical objects. The binary string. may represent an abstract concept, such as the number 40 711 597, but the binary symbols 0 and...

We present an excerpt of the document “Quantum Information Processing and Communication: Strategic report on current status, visions and goals for research in Europe”, which has been recently published in electronic form at the website of FET (the Future and Emerging Technologies Unit of the Directorate General Information Society of the Europ...

Almost all computational tasks in the modern computer can be designed from basic building blocks. These building blocks provide a powerful and efficient language for describing algorithms. In quantum computers, the basic building blocks are the quantum gates. In this tutorial, we will look at quantum gates that act on one and two qubits and briefly...

This is a collection of statements gathered on the occasion of the Quantum Physics of Nature meeting in Vienna.

When prior partial information about a state to be cloned is available, it can be cloned with a fidelity higher than that of universal quantum cloning. We experimentally verify this intriguing relationship between the cloning fidelity and the prior information by reporting the first experimental optimal quantum state-dependent cloner, using nuclear...

We derive a tight upper bound for the fidelity of a universal N → M qubit cloner, valid for any M ≥ N, where the output of the cloner is required to be supported on the symmetric subspace. Our proof is based on the concatenation of two cloners and the connection between quantum cloning and quantum state estimation. We generalize the operation of a...

Almost all computational tasks in, the modem computer can be designed from basic building blocks. These building blocks provide a powerful and efficient language for describing algorithms. In quantum computers, the basic building blocks are the quantum gates. In this tutorial, we will look at quantum gates that act on one and two qubits and briefly...

Transfer of data in linear quantum registers can be significantly simplified with preengineered but not dynamically controlled interqubit couplings. We show how to implement a mirror inversion of the state of the register in each excitation subspace with respect to the center of the register. Our construction is especially appealing as it requires...

We experimentally demonstrate in NMR a quantum interferometric multi-meter for extracting certain properties of unknown quantum states without resource to quantum tomography. It can perform direct state determinations, eigenvalue/eigenvector estimations, purity tests of a quantum system, as well as the overlap of any two unknown quantum states. Usi...

We propose a class of qubit networks that admit perfect state transfer of any two-dimensional quantum state in a fixed period of time. We further show that such networks can distribute arbitrary entangled states between two distant parties, and can, by using such systems in parallel, transmit the higher dimensional systems states across the network...

We present a class of spin networks that act as perfect quantum wires—quantum states transfer across these networks with unit fidelity in a time proportional to the network’s size. No couplings need to be switched on and off during this process. We prove that N‐spin hypercube networks with equal‐strength nearest‐neighbor Heisenberg and XY couplings...

We study the occurrence of multipartite entanglement in spin chains. We show that certain genuine multipartite entangled states, namely W states, can be obtained as ground states of simple XX type ferromagnetic spin chains in a transverse magnetic field, for any number of sites. Moreover, multipartite entanglement is proven to exist even at finite...

Quantum computers require technologies that offer both sufficient control over coherent quantum phenomena and minimal spurious interactions with the environment. We argue that, photons confined to photonic crystals, and in particular to highly efficient waveguides formed by linear chains of defects, doped with atoms or quantum dots, can generate st...

We propose an experiment to observe interference of a single electron as it is transported along two parallel quasi-one-dimensional channels trapped in a single minimum of a travelling periodic electric field. The experimental device is a modification of the surface acoustic wave (SAW) based quantum processor. Interference is achieved by creating a...

We propose a class of qubit networks that admit the perfect state transfer of any quantum state in a fixed period of time. Unlike many other schemes for quantum computation and communication, these networks do not require qubit couplings to be switched on and off. When restricted to N-qubit spin networks of identical qubit couplings, we show that 2...

Quantum key distribution allows two parties, traditionally known as Alice and Bob, to establish a secure random cryptographic key if, rstly, they have access to a quantum communication channel, and secondly, they can exchange classical public messages which can be monitored but not altered by an eavesdropper, Eve. Quantum key distribution provides...

Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. It has recently been shown that this problem is NP-hard. There is a highly inefficient `basic algorithm' for solving the quantum separability problem which follows from the definition of a separable state. By exploiti...

Contents 1 Qubits, gates and networks 2 Quantum arithmetic and function evaluations 3 Algorithms and their complexity 4 From interferometers to computers 5 The first quantum algorithms 6 Quantum search 7 Optimal phase estimation 8 Periodicity and quantum factoring 9 Cryptography 10 Conditional quantum dynamics 11 Decoherence and recoherence 12 Conc...

An abstract is not available.

We describe a nuclear magnetic resonance (NMR) experiment which implements an efficient one-to-two qubit phase-covariant cloning machine(QPCCM). In the experiment we have achieved remarkably high fidelities of cloning, 0.848 and 0.844 respectively for the original and the blank qubit. This experimental value is close to the optimal theoretical valu...

Examples of geometric phases abound in many areas of physics. They offer both fundamental insights into many physical phenomena and lead to interesting practical implementations. One of them, as indicated recently, might be an inherently fault-tolerant quantum computation. This, however, requires one to deal with geometric phases in the presence of...

We present an application of particle statistics to the problem of optimal ambiguous discrimination of quantum states. The states to be discriminated are encoded in the internal degrees of freedom of identical particles, and we use the bunching and antibunching of the external degrees of freedom to discriminate between various internal states. We s...

The security of a cryptographic key that is generated by communication through a noisy quantum channel relies on the ability to distill a shorter secure key sequence from a longer insecure one. For an important class of protocols, which exploit tomographically complete measurements on entangled pairs of any dimension, we show that the noise thresho...

After playing a significant role in the development of the foundations of quantum mechanics, entanglement has been recently rediscovered as a new physical resource with potential commercial applications, ranging from quantum cryptography to very precise frequency standards. Thus, the detection of quantum entanglement is vital in the experimental co...

Both direct spectrum estimations and the structural physical approximations which can be implemented in the case of bipartite states using only local operations and classical communications were demonstrated. This lead to more direct, local operations and communicate classically (LOCC) type, detections and estimations of quantum entanglement and of...

We present a cryptographic protocol based upon entangled qutrit pairs. We analyze the scheme under a symmetric incoherent attack and plot the region for which the protocol is secure and compare this with the region of violations of certain Bell inequalities.

Several results on local decompositions of witnesses for different situations are presented. Witnesses detecting NPT states in bipartite systems of N × M dimensions are considered and bounds on the minimal number of needed local measurements are given. In this way some of decompositions are proved to be optimal. Similar analysis is performed for bo...

A Reply to the Comment by R. Bhandari.

In this paper we address the problem of detection of entanglement using only few local measurements when some knowledge about the state is given. The idea is based on an optimized decomposition of witness operators into local operators. We discuss two possible ways of optimizing this local decomposition. We present several analytical results and es...

Basing on positive maps separability criterion we propose the experimentally viable, direct detection of quantum entanglement. It is efficient and does not require any a priori knowledge about the state. For two qubits it provides a sharp (i.e., "if and only if") separability test and estimation of amount of entanglement. We view this method as a n...

A computation is a physical process. It may be performed by a piece of electronics or on an abacus, or in your brain, but it is a process that takes place in nature and as such it is subject to the laws of physics. Quantum computers are machines that rely on characteristically quantum phenomena, such as quantum interference and quantum entanglement...

We describe how quantum entanglement can be used in secure communication.

We present a simple quantum network, based on the controlled-SWAP gate, that can extract certain properties of quantum states without recourse to quantum tomography. It can be used as a basic building block for direct quantum estimations of both linear and nonlinear functionals of any density operator. The network has many potential applications ra...

We introduce a general method for the experimental detection of entanglement by performing only few local measurements, assuming some prior knowledge of the density matrix. The idea is based on the minimal decomposition of witness operators into a pseudo-mixture of local operators. We discuss an experimentally relevant case of two qubits, and show...

We present a simple quantum network, based on the controlled-SWAP gate, that can extract certain properties of quantum states without recourse to quantum tomography. It can be used used as a basic building block for direct quantum estimations of both linear and non-linear functionals of any density operator. The network has many potential applicati...

The precision of frequency measurements performed on trapped ions in the presence of decoherence is analysed. In particular, standard Ramsey spectroscopy on uucorrelated ions and optimal measurements on maximally entangled states are proved to lead to the same resolution, while the best precision is achieved using partially entangled preparations....

In 1935 Albert Einstein together with Boris Podolsky and Nathan Rosen (EPR) published a paper in which they outlined how a ‘proper’ fundamental theory of nature should look like [1]. The EPR programme required completeness (“In a complete theory there is an element corresponding to each element of reality”), locality (“The real factual situation of...

We present a simple device based on the controlled-SWAP gate that performs quantum state tomography. It can also be used to determine maximum and minimum eigenvalues, expectation values of arbitrary observables, purity estimation as well as characterizing quantum channels. The advantage of this scheme is that the architecture is fixed and the task...

The only difference between Bhandari's viewpoint [quant-ph/0108058] and ours [Phys. Rev. Lett. 85, 2845 (2000)] is that our phase is defined modulo $2\pi$, whereas Bhandari argues that two phases that differ by $2\pi n$, $n$ integer, may be distinguished experimentally in a history-dependent manner. Comment: 2 pages