A. C. de la Torre, D. Goyeneche, L. Leitao
It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom, becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is ubiquitous in quantum systems. Simple examples are calculated and a general proof is provided. The physical relevance of the change of tensor product structure is mentioned.
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We construct quantum games from a table of non-factorizable joint probabilities, coupled with a symmetry constraint, requiring symmetrical payoffs between the players. We give the general result for a Nash equilibrium and payoff relations for a game based on non-factorizable joint probabilities, which embeds the classical game. We study a quantum version of Prisoners' Dilemma, Stag Hunt, and the Chicken game constructed from a given table of non-factorizable joint probabilities to find new outcomes in these games. We show that this approach provides a general framework for both classical and q…
A game-theoretic setting provides a mathematical basis for analysis of strategic interaction among competing agents and provides insights into both classical and quantum decision theory and questions of strategic choice. An outstanding mathematical question, is to understand the conditions under which a classical game-theoretic setting can be transformed to a quantum game, and under which conditions there is an equivalence. In this paper, we consider quantum games as those that allow non-factorizable probabilities. We discuss two approaches for obtaining a non-factorizable game and study the o…
We use the standard three-party Einstein-Podolsky-Rosen (EPR) setting in order to play general three-player non-cooperative symmetric games. We analyze how the peculiar non-factorizable joint probabilities that may emerge in the EPR setting can change outcome of the game. Our setup requires that the quantum game attains classical interpretation for factorizable joint probabilities. We analyze the generalized three-player game of Prisoner's Dilemma (PD) and show that the players can indeed escape from the classical outcome of the game because of non-factorizable joint probabilities. This result…
A probabilistic framework is developed that gives a unifying perspective on both the classical and the quantum games. We suggest exploiting peculiar probabilities involved in Einstein-Podolsky-Rosen (EPR) experiments to construct quantum games. In our framework a game attains classical interpretation when joint probabilities are factorizable and a quantum game corresponds when these probabilities cannot be factorized. We analyze how non-factorizability changes Nash equilibria in two-player games while considering the games of Prisoner's Dilemma, Stag Hunt, and Chicken. In this framework we fin…
The well known refinement of the Nash Equilibrium (NE) called an Evolutionarily Stable Strategy (ESS) is investigated in the quantum Prisoner's Dilemma (PD) game that is played using an Einstein-Podolsky-Rosen type setting. Earlier results report that in this scheme the classical NE remains intact as the unique solution of the quantum PD game. In contrast, we show here that interestingly in this scheme a non-classical solution for the ESS emerges for the quantum PD.
We demonstrate that any pure bipartite state of two qubits may be decomposed into a superposition of a maximally entangled state and an orthogonal factorizable one. Although there are many such decompositions, the weights of the two superposed states are, remarkably, unique. We propose a measure of entanglement based on this decomposition. We also demonstrate that this measure is connected to three measures of entanglement previously set forth: maximal violation of Bell's inequality, concurrence, and two-particle visibility.
An error avoiding quantum code is presented which is capable of stabilizing Grover's quantum search algorithm against a particular class of coherent errors. This error avoiding code consists of states only which are factorizable in the computational basis. Furthermore, its redundancy is smaller than the one which is achievable with a general error correcting quantum code saturating the quantum Hamming bound. The fact that this code consists of factorizable states only may offer advantages for the implementation of quantum gates in the error free subspace.
Entanglement Before Spacetime in Quantum-Gravity-Induced Interactions
该研究在形式不变的扭矢框架中重新表述了量子引力诱导纠缠，揭示了牛顿相的产生依赖于时空几何的破坏。
We demonstrate a general method of engineering the joint quantum state of photon pairs produced in spontaneous parametric downconversion (PDC). The method makes use of a superlattice structure of nonlinear and linear materials, in conjunction with a broadband pump, to manipulate the group delays of the signal and idler photons relative to the pump pulse, and realizes a joint spectral amplitude with arbitrary degree of entanglement for the generated pairs. This method of group delay engineering has the potential of synthesizing a broad range of states including factorizable states crucial for q…
We introduce a new class of non-local games, and corresponding densities, which we call bisynchronous. Bisynchronous games are a subclass of synchronous games and exhibit many interesting symmetries when the algebra of the game is considered. We develop a close connection between these non-local games and the theory of quantum groups which recently surfaced in studies of graph isomorphism games. When the number of inputs is equal to the number of outputs, we prove that a bisynchronous density arises from a trace on the quantum permutation group. Each bisynchronous density gives rise to a compl…
In this brief paper, starting from recent works, we analyze from conceptual point of view this basic question: can the nature of quantum entangled states be interpreted ontologically or epistemologically? According to some works, the degrees of freedom (and the tool of quantum partitions) of quantum systems permit us to establish a possible classification between factorizable and entangled states. We suggest, that the "choice" of degree of freedom (or quantum partitions), even if mathematically justified introduces an epistemic element, not only in the systems but also in their classification.…
Entangled quantum trajectories in relativistic systems
针对相对论场景下不同惯性系量子粒子纠缠的研究难题，本文提出基于多时间轨迹与约束欧拉-拉格朗日方程的框架，可量化纠缠的动力学及相对论影响，为星地量子通信等场景的相对论纠缠研究提供新方法。
Mixed-State Entanglement in a Minimal Model of Quantum Chaos
研究量子多体系统中混合态纠缠的传播，结合复制技巧与时空对称性，确定部分转置的减少密度矩阵谱，并发现早期时间的纠缠负性、奇数熵和Rényi互信息的精确关系。
This paper discusses relationships between topological entanglement and quantum entanglement. Specifically, we propose that for this comparison it is fundamental to view topological entanglements such as braids as "entanglement operators" and to associate to them unitary operators that are capable of creating quantum entanglement.
It is shown that Smolin four-qubit bound entangled states [Phys. Rev. A, 63 032306 (2001)] can maximally violate two-setting Bell inequality similar to standard CHSH inequality. Surprisingly this entanglement does not allow for secure key distillation, so neither entanglement nor violation of Bell inequalities implies quantum security. It is also pointed out how that kind of bound entanglement can be useful in reducing communication complexity.
Using entanglement of assistance, we establish a general polygamy inequality of multi-party entanglement in arbitrary dimensional quantum systems. For multi-party closed quantum systems, we relate our result with the monogamy of entanglement to show that the entropy of entanglement is an universal entanglement measure that bounds both monogamy and polygamy of multi-party quantum entanglement.
PhD thesis dealing with various aspects of multipartite entanglement, such as entanglement measures, absolutely maximally entangled states, bell inequalities, entanglement spectrum and quantum frustration. Also some quantum algorithms run with the IBM quantum computer are covered, together with others applied to adiabatic quantum computation and quantum thermodynamics.
The degree of entanglement in an open quantum system varies according to how information in the environment is read. A measure of this contextual entanglement is introduced based on quantum trajectory unravelings of the open system dynamics. It is used to characterize the entanglement in a driven quantum system of dimension $2\times\infty$ where the entanglement is induced by the environmental interaction. A detailed mechanism for the environment-induced entanglement is given.
It is known that if the quantum gates in a proposed quantum computer are so noisy that they are incapable of generating entanglement, then the device can be efficiently simulated classically. If the measurements and single particle operations are restricted, then the same statement can be true for generalised non-quantum notions of entanglement. Here we show that this can improve the applicability of limited-entanglement simulation algorithms. In particular, we show that by using a non-quantum notion of separability a classical simulation algorithm of Harrow & Nielsen can efficiently simulate …
Entanglement is a key issue in the quantum physics which gives rise to resources for achieving tasks that are not possible within the realm of classical physics. Quantum entanglement varies with the evolution of the quantum systems. It is of significance to investigate the entanglement dynamics in terms of quantum channels. We study the entanglement-breaking channels and present the necessary and sufficient conditions for a quantum channel to an entanglement-breaking one for qubit systems. Furthermore, a concept of strong entanglement-breaking channel is introduced. The amendment of entangleme…
Recovering quantum entanglement after its certification
针对量子纠缠认证会破坏纠缠资源的问题，提出一种可概率恢复原始纠缠的认证协议，在光子系统实验验证其筛选高质量纠缠的实用性，揭示相关物理量的权衡关系，实现认证与后续应用兼容。
Role of qubits in quantum entanglement and quantum teleportation
本文探讨了量子比特在量子纠缠和量子 teleportation 中的关键作用与重要性。
We relate the problem of irreversibility of entanglement with the recently defined measures of quantum correlation - quantum discord and one-way quantum deficit. We show that the entanglement of formation is always strictly larger than the coherent information and the entanglement cost is also larger in most cases. We prove irreversibility of entanglement under LOCC for a family of entangled states. This family is a generalization of the maximally correlated states for which we also give an analytic expression for the distillable entanglement, the relative entropy of entanglement, the distilla…
We investigate the entanglement features of the quantum states employed in quantum algorithms. In particular, we analyse the multipartite entanglement properties in the Deutsch-Jozsa, Grover and Simon algorithms. Our results show that for these algorithms most instances involve multipartite entanglement.
This paper gives a criterion for detecting the entanglement of a quantum state, and uses it to study the relationship between topological and quantum entanglement. It is fundamental to view topological entanglements such as braids as entanglement operators and to associate to them unitary operators that are capable of creating quantum entanglement. The entanglement criterion is used to explore this connection. The paper discusses non-locality in the light of this criterion.
We consider the standard quantum teleportation protocol where a general bipartite state is used as entanglement resource. We use the entanglement fidelity to describe how well the standard quantum teleportation channel transmits quantum entanglement and give a simple expression for the entanglement fidelity when it is averaged on all input states.
We point out that density matrices can only be used to describe quantum states, so the entanglement contained in a density matrix is just quantum entanglement. This means a bipartite state described by a density matrix contains quantum entanglement, unless the density matrix has the form $ρ_{AB}=ρ_A\otimes ρ_B$.
Three inter-related topics are discussed here. One, the Lindblad dynamics of quantum dissipative systems; two, quantum entanglement in composite systems and its quantification based on the Tsallis entropy; and three, robustness of entanglement under dissipation. After a brief review of the Lindblad theory of quantum dissipative systems and the idea of quantum entanglement in composite quantum systems illustrated by describing the three particle systems, the behavior of entanglement under the influence of dissipative processes is discussed. These issues are of importance in the discussion of qu…
We simulate entanglement sharing between two end-nodes of a quantum network using SeQUeNCe, an open-source simulation package for quantum networks. Our focus is on the rate of entanglement generation between the end-nodes with many repeaters with a finite quantum memory lifetime. Our findings demonstrate that the performance of quantum connection depends highly on the entanglement management protocol scheduling entanglement generation and swapping, resulting in the final end-to-end entanglement. Numerical and analytical simulations show limits of connection performance for a given number of re…
Quantum transduction refers to the coherent conversion between microwave and optical states, which can be achieved by quantum teleportation if given high fidelity microwave-optical entanglement, namely entanglement-based quantum transduction. Reliable microwave-optical entanglement can be generated using various platforms. In this paper, we base the discussion on piezo-optomechanical system and make the teleportation induced conversion scheme more concrete in the framework of quantum channel theory. By comparing the quantum capacity between the entanglement-based conversion channel and the tra…
We show that bipartite entanglement distribution (or entanglement of assistance) in multipartite quantum systems is by nature polygamous. We first provide an analytic upper bound for the concurrence of assistance in bipartite quantum systems, and derive a polygamy inequality of multipartite entanglement in arbitrary dimensional quantum systems.
We review the criteria for separability and quantum entanglement, both in a bipartite as well as a multipartite setting. We discuss Bell inequalities, entanglement witnesses, entropic inequalities, bound entanglement and several features of multipartite entanglement. We indicate how these criteria bear on the experimental detection of quantum entanglement.
We provide several formulas that determine the optimal number of entangled bits (ebits) that a general entanglement-assisted quantum code requires. Our first theorem gives a formula that applies to an arbitrary entanglement-assisted block code. Corollaries of this theorem give formulas that apply to a code imported from two classical binary block codes, to a code imported from a classical quaternary block code, and to a continuous-variable entanglement-assisted quantum block code. Finally, we conjecture two formulas that apply to entanglement-assisted quantum convolutional codes.
Entanglement measures quantify the amount of quantum entanglement that is contained in quantum states. Typically, different entanglement measures do not have to be partially ordered. The presence of a definite partial order between two entanglement measures for all quantum states, however, allows for meaningful conceptualization of sensitivity to entanglement, which will be greater for the entanglement measure that produces the larger numerical values. Here, we have investigated the partial order between the normalized versions of four entanglement measures based on Schmidt decomposition of bi…
We discuss maximum entangled states of quantum systems in terms of quantum fluctuations of all essential measurements responsible for manifestation of entanglement. Namely, we consider maximum entanglement as a property of states, for which quantum fluctuations come to their extreme.
Entanglement is an essential resource in current experimental implementations for quantum information processing. We review a class of experiments exploiting photonic entanglement, ranging from one-way quantum computing over quantum communication complexity to long-distance quantum communication. We then propose a set of feasible experiments that will underline the advantages of photonic entanglement for quantum information processing.
Twenty-five years after the invention of quantum teleportation, the concept of entanglement gained enormous popularity. This is especially nice to those who remember that entanglement was not even taught at universities until the 1990's. Today, entanglement is often presented as a resource, the resource of quantum information science and technology. However, entanglement is exploited twice in quantum teleportation. First, entanglement is the `quantum teleportation channel', i.e. entanglement between distant systems. Second, entanglement appears in the eigenvectors of the joint measurement that…
Entanglement of quantum variables is usually thought to be a prerequisite for obtaining quantum speed-ups of information processing tasks such as searching databases. This paper presents methods for quantum search that give a speed-up over classical methods, but that do not require entanglement. These methods rely instead on interference to provide a speed-up. Search without entanglement comes at a cost: although they outperform analogous classical devices, the quantum devices that perform the search are not universal quantum computers and require exponentially greater overhead than a quantum …
Quantum measurement is a class of quantum channels that sends quantum states to classical states. We set up resource theories of quantum coherence and quantum entanglement for quantum measurements and find relations between them. For this, we conceive a relative entropy type quantity to account for the quantum resources of quantum measurements. The quantum coherence of a quantum measurement can be converted into the entanglement in a bipartite quantum measurement through coherence-non generating transformations. Conversely, a quantum entanglement monotone of quantum measurements induces a quan…
We investigate the average bipartite entanglement, over all possible divisions of a multipartite system, as a useful measure of multipartite entanglement. We expose a connection between such measures and quantum-error-correcting codes by deriving a formula relating the weight distribution of the code to the average entanglement of encoded states. Multipartite entangling power of quantum evolutions is also investigated.
We study the Bell nonlocality of high dimensional quantum systems based on quantum entanglement. A quantitative relationship between the maximal expectation value B of Bell operators and the quantum entanglement concurrence C is obtained for even dimension pure states, with the upper and lower bounds of B governed by C.
We examine several well known quantum spin models and categorize behavior of pairwise entanglement at quantum phase transitions. A unified picture on the connection between the entanglement and quantum phase transition is given.
PhD thesis (University of York). The thesis covers in a unified way the material presented in quant-ph/0403073, quant-ph/0502040, quant-ph/0504160, quant-ph/0510035, quant-ph/0512012 and quant-ph/0603283. It includes two large review chapters on entanglement and distillation.
We study entanglement properties of all eigenstates of the Heisenberg XXX model, and find that the entanglement and mixedness for a pair of nearest-neighbor qubits are completely determined by the corresponding eigenenergies. Specifically, the negativity of the eigenenergy implies pairwise entanglement. From the relation between entanglement and eigenenergy, we obtain finite-size behaviors of the entanglement. We also study entanglement and mixedness versus energy in the quantum Heisenberg XY model.
With Hubbard model, the entanglement scaling behavior in a two-dimensional itinerant system is investigated. It has been found that, on the two sides of the critical point denoting an inherent quantum phase transition (QPT), the entanglement follows different scalings with the size just as an order parameter does. This fact reveals the subtle role played by the entanglement in QPT as a fungible physical resource.
Comment on "Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit" The effective absorption rates in quantum lithography are very low.
The entanglement of formation gives a necessary and sufficient condition for the existence of a perfect quantum error correction procedure.
Genuine multipartite entanglement plays important roles in quantum information processing. The detection of genuine multipartite entanglement has been long time a challenging problem in the theory of quantum entanglement. We propose a criterion for detecting genuine tripartite entanglement of arbitrary dimensional tripartite states based on quantum Fisher information. We show that this criterion is more effective for some states in detecting genuine tripartite entanglement by detailed example.
The non-Markovian dynamics of quantum entanglement is studied by the Shabani-Lidar master equation when one of entangled quantum systems is coupled to a local reservoir with memory effects. The completely positive reduced dynamical map can be constructed in the Kraus representation. Quantum entanglement decays more slowly in the non-Markovian environment. The decoherence time for quantum entanglement can be markedly increased by the change of the memory kernel. It is found out that the entanglement sudden death between quantum systems and entanglement sudden birth between the system and reserv…
The quantum entanglement is considered as one of the most important notions of quantum computing. The entanglement is a feature of quantum systems and it is used as a basis for many quantum algorithms and protocols. In this paper we analyze the level of entanglement for the quantum switch, during its work. The level of entanglement during the correct operating may be compared with the situation when a noise is present in the analyzed system. The noise changes the level of quantum entanglement and we utilize this observation to evaluate if the switch works properly. We present the formulae desc…
Quantum entanglement is a critical resource for quantum information and quantum computation. However, entanglement of a quantum system is subjected to change due to the interaction with the environment. One typical result of the interaction is the amplitude damping that usually results in the reduction of the entanglement. Here we propose a protocol to protect quantum entanglement from the amplitude damping by applying Hadamard and CNOT gates. As opposed to some recently studied methods, the scheme presented here does not require weak measurement in the reversal process, leading to a faster re…
We provide a sufficient condition for the monogamy inequality of multi-party quantum entanglement of arbitrary dimensions in terms of entanglement of formation. Based on the classical-classical-quantum(ccq) states whose quantum parts are obtained from the two-party reduced density matrices of a three-party quantum state, we show the additivity of the mutual information of the ccq states guarantees the monogamy inequality of the three-party pure state in terms of EoF. After illustrating the result with some examples, we generalize our result of three-party systems into any multi-party systems o…
The entanglement measure for multiqudits is proposed. This measure calculates the partial entanglement distributed by subsystems and the complete entanglement of the total system. This shows that we need to measure the subsystem entanglements to explain the full description for multiqudit entanglement. Furthermore, we extend the entanglement measure to mixed multiqubits and the higher dimension Hilbert spaces.
This is a thesis submitted to university of Pune, India, for the Ph.D. degree. This work deals with entanglement production in two qubit, two qutrit and three qubit systems, entanglement in indistinguishable fermionic systems, quantum discord in a Heisenberg chain and geometric measure of quantum discord in an arbitrary state of a bipartite quantum system.
The entanglement fidelity provides a measure of how well the entanglement between two subsystems is preserved in a quantum process. By using a simple model we show that in some cases this quantity in its original definition fails in the measurement of the entanglement preserving. On the contrary, the modified entanglement fidelity, obtained by using a proper local unitary transformation on a subsystem, is shown to exhibit the behavior similar to that of the concurrence in the quantum evolution.
I explore entanglement dynamics in examples of quantum memories, decoherence free subspaces (DFS) and noiseless subsystems (NS), to determine how a complete loss of entanglement affects the ability of these techniques to protect quantum information. Using negativity and concurrence as entanglement measures, I find that in general there is no correlation between the complete loss of entanglement in the system and the fidelity of the stored quantum information. These results complement previous results in which quantum protocols not explictly based on entanglement exhibit little correlation betw…
We give a review on entanglement purification for bipartite and multipartite quantum states, with the main focus on theoretical work carried out by our group in the last couple of years. We discuss entanglement purification in the context of quantum communication, where we emphasize its close relation to quantum error correction. Various bipartite and multipartite entanglement purification protocols are discussed, and their performance under idealized and realistic conditions is studied. Several applications of entanglement purification in quantum communication and computation are presented, w…
We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard quantum error correcting codes, thus allowing us to ``quantize'' all of classical linear coding theory. In particular, efficient modern classical codes that attain the Shannon capacity can be made into entanglement-assisted quantum codes attaining the hashing bound (closely related to the quantum capacity). For systems without large amounts of shared entanglement,…
Entanglement constitutes a key characteristic feature of quantum matter. Its detection, however, still faces major challenges. In this letter, we formulate a framework for probing entanglement based on machine learning techniques. The central element is a protocol for the generation of statistical images from quantum many-body states, with which we perform image classification by means of convolutional neural networks. We show that the resulting quantum entanglement recognition task is accurate and can be assigned a well-controlled error across a wide range of quantum states. We discuss the po…
Multipartite entanglement is of important resources for quantum communication and quantum computation. Our goal in this paper is to characterize general multipartite entangled states according to shallow quantum circuits. We firstly prove any genuinely multipartite entanglement on finite-dimensional spaces can be generated by using 2-layer shallow quantum circuit consisting of two biseparable quantum channels, which the smallest nontrivial circuit depth in the shallow quantum circuit model. We further propose a semi-device-independent entanglement model depending on the local connection abilit…
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