We give an explicit family of XOR games with O(n)-bit questions requiring 2^n ebits to play near-optimally. More generally we introduce a new technique for proving lower bounds on the amount of entanglement required by an XOR game: we show that near-optimal strategies for an XOR game G correspond to approximate representations of a certain C^*-algebra associated to G. Our results extend an earlier theorem of Tsirelson characterising the set of quantum strategies which implement extremal quantum correlations.
We show that for any $\varepsilon>0$ there is an XOR game $G=G(\varepsilon)$ with $Θ(\varepsilon^{-1/5})$ inputs for one player and $Θ(\varepsilon^{-2/5})$ inputs for the other player such that $Ω(\varepsilon^{-1/5})$ ebits are required for any strategy achieving bias that is at least a multiplicative factor $(1-\varepsilon)$ from optimal. This gives an exponential improvement in both the number of inputs or outputs and the noise tolerance of any previously-known self-test for highly entangled states. Up to the exponent $-1/5$ the scaling of our bound with $\varepsilon$ is tight: for any XOR g…
Suppose Alice and Bob make local two-outcome measurements on a shared entangled state. For any d, we show that there are correlations that can only be reproduced if the local dimension is at least d. This resolves a conjecture of Brunner et al. Phys. Rev. Lett. 100, 210503 (2008) and establishes that the amount of entanglement required to maximally violate a Bell inequality must depend on the number of measurement settings, not just the number of measurement outcomes. We prove this result by establishing the first lower bounds on a new generalization of Grothendieck's constant.
XOR games are a simple computational model with connections to many areas of complexity theory. Perhaps the earliest use of XOR games was in the study of quantum correlations. XOR games also have an interesting connection to Grothendieck's inequality, a fundamental theorem of analysis, which shows that two players sharing entanglement can achieve at most a constant factor advantage over players following classical strategies in an XOR game. Perez-Garcia et al. show that when the players share GHZ states, this advantage is bounded by a constant. We use a multilinear generalization of Grothendie…
We introduce quantum XOR games, a model of two-player one-round games that extends the model of XOR games by allowing the referee's questions to the players to be quantum states. We give examples showing that quantum XOR games exhibit a wide range of behaviors that are known not to exist for standard XOR games, such as cases in which the use of entanglement leads to an arbitrarily large advantage over the use of no entanglement. By invoking two deep extensions of Grothendieck's inequality, we present an efficient algorithm that gives a constant-factor approximation to the best performance play…
In this paper we show that, given $k\geq 3$, there exist $k$-player quantum XOR games for which the entangled bias can be arbitrarily larger than the bias of the game when the players are restricted to separable strategies. In particular, quantum entanglement can be a much more powerful resource than local operations and classical communication to play these games. This result shows a strong contrast to the bipartite case, where it was recently proved that the entangled bias is always upper bounded by a universal constant times the one-way classical communication bias.
In this work we give an example of exponential separation between quantum and classical resources in the setting of XOR games assisted with communication. Specifically, we show an example of a XOR game for which $O(n)$ bits of two way classical communication are needed in order to achieve the same value as can be attained with $\log n$ qubits of one way communication. We also find a characterization for the value of a XOR game assisted with a limited amount of two way communication in terms of tensor norms of normed spaces.
The non-local game scenario provides a powerful framework to study the limitations of classical and quantum correlations, by studying the upper bounds of the winning probabilities those correlations offer in cooperation games where communication between players is prohibited. Building upon results presented in the seminal work of Cleve et al. [1], a straightforward construction to compute the Tsirelson bounds for simple 2-player XOR games is presented. The construction is applied explicitly to some examples, including the Entanglement Assisted Orientation in Space (EAOS) game of Brukner et al.…
We consider quantum XOR games, defined in [11], from the perspective of unitary correlations defined in [7]. We show that Connes' embedding problem has a positive answer if and only if every quantum XOR game has entanglement bias equal to the commuting bias. In particular, the embedding problem is equivalent to determining whether every quantum XOR game $G$ with a winning strategy in the commuting model also has a winning strategy in the approximate finite-dimensional model.
XOR games are the simplest model in which the nonlocal properties of entanglement manifest themselves. When there are two players, it is well known that the bias --- the maximum advantage over random play --- of entangled players can be at most a constant times greater than that of classical players. Recently, Pérez-García et al. [Comm. Math. Phys. 279 (2), 2008] showed that no such bound holds when there are three or more players: the advantage of entangled players over classical players can become unbounded, and scale with the number of questions in the game. Their proof relies on non-trivia…
Quantum conference is a process of securely exchanging messages between three or more parties, using quantum resources. A Measurement Device Independent Quantum Dialogue (MDI-QD) protocol, which is secure against information leakage, has been proposed (Quantum Information Processing 16.12 (2017): 305) in 2017, is proven to be insecure against intercept-and-resend attack strategy. We first modify this protocol and generalize this MDI-QD to a three-party quantum conference and then to a multi-party quantum conference. We also propose a protocol for quantum multi-party XOR computation. None of th…
Here we study multiplayer linear games, a natural generalization of XOR games to multiple outcomes. We generalize a recently proposed efficiently computable bound, in terms of the norm of a game matrix, on the quantum value of 2-player games to linear games with $n$ players. As an example, we bound the quantum value of a generalization of the well-known CHSH game to $n$ players and $d$ outcomes. We also apply the bound to show in a simple manner that any nontrivial functional box, that could lead to trivialization of communication complexity in a multiparty scenario, cannot be realized in quan…
We consider quantum computing with pseudo-pure states. This framework arises in certain implementations of quantum computing using NMR. We analyze quantum computational protocols which aim to solve exponential classical problems with polynomial resources and ask whether or not entanglement of the pseudo-pure states is needed to achieve this aim. We show that for a large class of such protocols, including Shor's factorization, entanglement is necessary. We also show that achieving entanglement is not sufficient: if the noise in the state is sufficiently large, exponential resources are needed e…
The dynamics of a quantum XOR gate operation in a two-qubit system being coupled to a bath of quantum harmonic oscillators is investigated. Upon applying the numerical quasiadiabatic propagator path integral method, we obtain the numerically precise time-resolved evolution of this interacting two-qubit system in presence of time-dependent external fields without further approximations. We simulate the dissipative gate operation for characteristic experimental realizations of condensed matter qubits; namely, the flux and charge qubits realized in superconducting Josephson systems and qubits for…
A physical theory is called non-local when observers can produce instantaneous effects over distant systems. Non-local theories rely on two fundamental effects: local uncertainty relations and steering of physical states at a distance. In quantum mechanics, the former one dominates the other in a well-known class of non-local games known as XOR games. In particular, optimal quantum strategies for XOR games are completely determined by the uncertainty principle alone. This breakthrough result has yielded the fundamental open question whether optimal quantum strategies are always restricted by l…
We consider an evolution of two elementary quantum particles and ask the question: under what conditions such a system behaves as a single object? It is obvious that if the attraction between the particles is stronger than any other force acting on them the whole system behaves as one. However, recent insight from the quantum information theory suggests that in bipartite systems it is not attraction per se that is responsible for the composite nature, but the entanglement between the parts. Since entanglement can be present between the subsystems that interacted in the past, but do not interac…
From a practical perspective it is advantageous to develop methods that verify entanglement in quantum states with as few measurements as possible. In this paper we investigate the minimal number of mutually unbiased bases (MUBs) needed to detect bound entanglement in bipartite $(d\times d)$-dimensional states, i.e. entangled states that are positive under partial transposition. In particular, we show that a class of entanglement witnesses composed of mutually unbiased bases can detect bound entanglement if the number of measurements is greater than $d/2+1$. This is a substantial improvement o…
Given a Hamiltonian that is a sum of commuting few-body terms, the commuting Hamiltonian problem is to determine if there exists a quantum state that is the simultaneous eigenstate of all of these terms that minimizes each term individually. This problem is known to be in the complexity class quantum Merlin-Arthur, but is widely thought to not be complete for this class. Here we show that a limited form of this problem when the individual terms are all made up of tensor products of Pauli matrices is efficiently solvable on a classical computer and thus in the complexity class P. The problem ca…
We show that the amount of entanglement needed as an initial resource to set up a certain final amount of entanglement between two ends of a noisy channel can be reduced in certain cases by using quantum repeaters. Our investigation (for various channels) considers cases when a large number of entangled pairs are transmitted through the channel using known asymptotic results and conjectured bounds on distillable entanglement.
A two-player one-round binary game consists of two cooperative players who each replies by one bit to a message that he receives privately; they win the game if both questions and answers satisfy some predetermined property. A game is called entangled if the players are allowed to share a priori entanglement. It is well-known that the maximum winning probability (value) of entangled XOR-games (binary games in which the predetermined property depends only on the XOR of the two output bits) can be computed by a semidefinite program. In this paper we extend this result in the following sense; if …
We present a dynamic learning paradigm for "programming" a general quantum computer. A learning algorithm is used to find the control parameters for a coupled qubit system, such that the system at an initial time evolves to a state in which a given measurement corresponds to the desired operation. This can be thought of as a quantum neural network. We first apply the method to a system of two coupled superconducting quantum interference devices (SQUIDs), and demonstrate learning of both the classical gates XOR and XNOR. Training of the phase produces a gate congruent to the CNOT modulo a phase…
We show why and when entanglement is needed for quantum-enhanced precision measurements, and which type of entanglement is useful. We give a simple, intuitive construction that shows how entanglement transforms parallel estimation strategies into sequential ones of same precision. We employ this argument to generalize conventional quantum metrology, to identify a class of noise whose effects can be easily managed, and to treat the case of indistinguishable probes (such as interferometry with light).
A black box with two input bits and two output bits is called a non-local PR box, if the XOR of the output bits equals the AND of the input bits. In a recent article, Cerf et al. show that Alice and Bob, using such a PR box, can effectively simulate entanglement without the need of communication. We show that an adaptation of a model due to Dirk Aerts, yields a realistic simulation of the non-local PR box without communication. Because the model is entirely realistic, it cannot violate relativistic constraints. Like a non-local box, it can be used to simulate the singlet state coincidence prob…
We bound separations between the entangled and classical values for several classes of nonlocal $t$-player games. Our motivating question is whether there is a family of $t$-player XOR games for which the entangled bias is $1$ but for which the classical bias goes down to $0$, for fixed $t$. Answering this question would have important consequences in the study of multi-party communication complexity, as a positive answer would imply an unbounded separation between randomized communication complexity with and without entanglement. Our contribution to answering the question is identifying sever…
Bound entanglement with a nonpositive partial transposition (NPT) does not exist. For any NPT entangled state a distillation procedure can be based on a certain number of copies. This number is the minimal Schmidt rank of a pure state needed to witness the NPT entanglement under study.
Here it is shown that the squashed entanglement has an operational meaning -- it is the fastest rate at which a quantum state can be sent between two parties who share arbitrary side-information. Likewise, the entanglement of formation and entanglement cost is shown to be the fastest rate at which a quantum state can be sent when the parties have access to side-information which is maximally correlated. A further restriction on the type of side-information implies that the rate of state transmission is given by the quantum mutual information. This suggests a new paradigm for understanding enta…
We report the exact entanglement cost of a class of multiqubit bound entangled states, computed in the context of a universal model for multipartite state preparation. The exact amount of entanglement needed to prepare such states are determined by first obtaining lower bounds using a cut-set approach, and then providing explicit local protocols achieving the lower bound.
We present an explicit construction of entanglement witnesses for depolarized states in arbitrary finite dimension. For infinite dimension we generalize the construction to twin-beams perturbed by Gaussian noises in the phase and in the amplitude of the field. We show that entanglement detection for all these families of states requires only three local measurements. The explicit form of the corresponding set of local observables (quorom) needed for entanglement witness is derived.
In this paper we describe how three qubit entanglement can be analyzed with local measurements. For this purpose we decompose entanglement witnesses into operators which can be measured locally. Our decompositions are optimized in the number of measurement settings needed for the measurement of one witness. Our method allows to detect true threepartite entanglement and especially GHZ-states with only four measurement settings.
The ``entanglement of formation'' of a mixed state of a bipartite quantum system can be defined in terms of the number of pure singlets needed to create the state with no further transfer of quantum information. We find an exact formula for the entanglement of formation for all mixed states of two qubits having no more than two non-zero eigenvalues, and we report evidence suggesting that the formula is valid for all states of this system.
We propose a method to implement a kind of non-local operations between spatially separated two systems with arbitrary high-dimensions by using only low-dimensional qubit quantum channels and classical bit communications. The result may be generalized straightforwardly to apply for multiple systems, each of them with arbitrary dimensions. Compared with existed approaches, our method can economize classical resources and the needed low-dimensional quantum channels may be more easily established in practice. We also show the construction of the non-local quantum XOR gate for qutrit systems in te…
This report is about contradiction between fidelity needed to determine the entanglement and concomitant noise that always accompanies precise measurement. Account of quantum properties of field leads to additional noise caused by multiple particle creation through nonunitarity of quantum field representation in embedded sections of space (Unruh noise). Causes of quantum noise vanish at leaving off assumption about statistical independence of detectors. Smearing of detector leads to elimination of causes of Unruh noise and to emergence of imaginary entanglement of few mode states caused by ove…
We apply the approach of verifying entanglement, which is based on the sole knowledge of the dimension of the underlying physical system to the entanglement based version of the BB84 quantum key distribution protocol. We show that the familiar one-way key rate formula holds already if one assumes the assumption that one of the parties is measuring a qubit and no further assumptions about the measurement are needed.
In this paper, we investigate how to reduce the number of measurement configurations needed for sufficiently precise entanglement quantification. Instead of analytical formulae, we employ artificial neural networks to predict the amount of entanglement in a quantum state based on results of collective measurements (simultaneous measurements on multiple instances of the investigated state). This approach allows us to explore the precision of entanglement quantification as a function of measurement configurations. For the purpose of our research, we consider general two-qubit states and their ne…
We report results bearing on the behavior of non-local decoherence and its potential for being managed or even controlled. The decoherence process known as entanglement sudden death (ESD) can drive prepared entanglement to zero at the same time that local coherences and fidelity remain non-zero. For a generic ESD-susceptible Bell superposition state, we provide rules restricting the occurrence and timing of ESD, amounting to management tools over a continuous variation of initial conditions. These depend on only three parameters: initial purity, entanglement and excitation. Knowledge or contro…
We build, using group-theoretic methods, a general framework for approaching multi-particle entanglement. As far as entanglement is concerned, two states of n spin-1/2 particles are equivalent if they are on the same orbit of the group of local rotations (U(2)^n). We give a method for finding the number of parameters needed to describe inequivalent n spin-1/2 particles states. We also describe how entanglement of states on a given orbit may be characterized by the stability group of the action of the group of local rotations on any point on the orbit.
We describe a direct method for experimental determination of the negativity of an arbitrary two-qubit state with 11 measurements performed on multiple copies of the two-qubit system. Our method is based on the experimentally accessible sequences of singlet projections performed on up to four qubit pairs. In particular, our method permits the application of the Peres-Horodecki separability criterion to an arbitrary two-qubit state. We explicitly demonstrate that measuring entanglement in terms of negativity requires three measurements more than detecting two-qubit entanglement. The reported mi…
We consider the random dimer model in one space dimension with Bernoulli disorder. For sufficiently small disorder, we show that the entanglement entropy exhibits at least a logarithmically enhanced area law if the Fermi energy coincides with a critical energy of the model where the localisation length diverges.
We derive a general framework to identify genuinely multipartite entangled mixed quantum states in arbitrary-dimensional systems and show in exemplary cases that the constructed criteria are stronger than those previously known. Our criteria are simple functions of the given quantum state and detect genuine multipartite entanglement that had not been identified so far. They are experimentally accessible without quantum state tomography and are easily computable as no optimization or eigenvalue evaluation is needed.
A quantum key distribution and identification protocol is proposed, which is based on entanglement swapping. Through choosing particles by twos from the sequence and performing Bell measurements, two communicators can detect eavesdropping, identify each other and obtain the secure key according to the measurement results. Because the two particles measured together are selected out randomly, we need neither alternative measurements nor rotation of the Bell states. Furthermore, less Bell measurements are needed in our protocol than in the previous similar ones.
We establish a framework to study the classical-communication properties of primitive local operations assisted by classical communication which realize various redistributions of entanglement, like, e.g., entanglement swapping. On the one hand, we analyze what local operations and how much classical communication are needed to perform them. On the other hand, we investigate whether and to what extent such primitives can help to establish classical communication when they are used in the form of black boxes available to spatially-separated users. In particular, we find that entanglement swappi…
We provide some new properties of entanglement of formation. In particular, we obtain an additive lower bound for entanglement of formation. Subsequently we develop the concept of local orthogonality of ensembles which leads to the mixed states with distillable entanglement equal to entanglement of formation. Then we consider thermodynamical analogies within the entanglement processing domain. Especially, we exploit analogy entanglement -- energy. In this scheme the total entanglement i.e. the amount of singlet pairs needed for local preparation of a state corresponds to internal energy while …
We discuss the realization of quantum advantage in a system without quantum entanglement but with non-zero quantum discord. We propose an optical realization of symmetric two-qubit $X$-states with controllable anti-diagonal elements. This approach does not requires initially entangled states, and it can generate states that have quantum discord, with or without entanglement. We discuss how quantum advantage can be attained in the context of a two-qubit game. We show that when entanglement is not present, the maximum quantum advantage is 1/3 bit. A comparable quantum advantage, 0.311 bit, can b…
We present our approach for sharing photons and assessing resultant four-photon visibility between two distant parties using concatenated entanglement swapping. In addition we determine the corresponding key generation rate and the quantum bit-error rate. Our model is based on practical limitations of resources, including multipair parametric down-conversion sources, inefficient detectors with dark counts and lossy channels. Through this approach, we have found that a trade-off is needed between experimental run-time, pair-production rate and detector efficiency. Concatenated entanglement swap…
We explore the relation between the entanglement of a pure state and its energy variance for a local one dimensional Hamiltonian, as the system size increases. In particular, we introduce a construction which creates a matrix product state of arbitrarily small energy variance $δ^2$ for $N$ spins, with bond dimension scaling as $\sqrt{N} D_0^{1/δ}$, where $D_0>1$ is a constant. This implies that a polynomially increasing bond dimension is enough to construct states with energy variance that vanishes with the inverse of the logarithm of the system size. We run numerical simulations to probe the …
It is known that entanglement swapping can be used to realize entanglement purifying. By this way, two particles belong to different non-maximally entangled pairs can be projected probabilisticly to a maximally entangled state or to a less entangled state. In this report, we show, when the less entangled state is obtained, if a unitary transformation is introduced locally, then a maximally entangled state can be obtained probabilisticly from this less entangled state. The total successful probability of our scheme is equal to the entanglement of a single pairpurification (if two original pairs…
Since the negative result of Lo (Physical Review A, 1997), it has been left open whether there exist some functions that can be securely computed in two-party setting in quantum domain when one of the parties is malicious. In this paper, we for the first time, show that there are some functions for which secure two-party quantum computation is indeed possible for non-simultaneous channel model. This is in sharp contrast with the impossibility result of Ben -Or et al. (FOCS, 2006) in broadcast channel model. The functions we study are of two types - one is any function without an embedded XOR, …
We propose a linear optical scheme for the teleportation of unknown ionic states, the entanglement concentration for nonmaximally entangled states for ions via entanglement swapping and the remote preparation for ionic entangled states. The unique advantage of the scheme is that the joint Bell-state measurement needed in the previous schemes is not needed in the current scheme, i.e. the joint Bell-state measurement has been converted into the product of separate measurements on single ions and photons. In addition, the current scheme can realize the quantum information processes for ions by us…
In this paper, we present a measure of multipartite entanglement ($k$-nonseparable), $k$-ME concurrence $C_{k-\mathrm{ME}}(ρ)$ that unambiguously detects all $k$-nonseparable states in arbitrary dimensions, where the special case, 2-ME concurrence $C_{2-\mathrm{ME}}(ρ)$, is a measure of genuine multipartite entanglement. The new measure $k$-ME concurrence satisfies important characteristics of an entanglement measure including entanglement monotone, vanishing on $k$-separable states, convexity, subadditivity and strictly greater than zero for all $k$-nonseparable states. Two powerful lower bou…
We show that the minimal rate of noise needed to catalytically erase the entanglement in a bipartite quantum state is given by the regularized relative entropy of entanglement. This offers a solution to the central open question raised in [Groisman, PRA 72, 032317 (2005)] and complements their main result that the minimal rate of noise needed to erase all correlations is given by the quantum mutual information. We extend our discussion to the tripartite setting where we show that an asymptotic rate of noise given by the regularized relative entropy of recovery is sufficient to catalytically tr…
We show how to distribute with percentage success probabilities almost perfectly entangled qubit memory pairs over repeater channel segments of the order of the optical attenuation distance. In addition to some weak, dispersive light-matter interactions, only Gaussian state transmissions and measurements are needed for this scheme, which even beats the coherent-state-benchmark for entanglement distribution based on error-free non-Gaussian measurements. This is achieved through two innovations: first, optical squeezed states are utilized instead of coherent states. Secondly, the amplitudes of t…
