通过设计量子库来调控量子比特间的Bell非定域性研究

量子系统间的Bell非定域性是一种比量子纠缠更为严格的量子关联,它在刻画多体量子关联有着不可或缺的作用.类似于量子纠缠,在开放两量子比特和三量子比特系统中的Bell非定域性可能会出现猝死现象.本文建议了一个可供选择的方案即在热库环境中通过增加辅助粒子来调控两量子比特和三量子比特间的Bell非定域性动力学.研究发现：通过调节辅助粒子数目,不仅两量子比特和三量子比特系统的Bell非定域性可以避免猝死现象的发生,而且在长时间极限下它能维持在一个较高水平.论文得到的结果将对多体量子系统间量子关联的调控和避免猝死现象等相关研究有积极的指导意义.     

Entanglement and nonlocality in multi-particle systems

Entanglement, the Einstein–Podolsky–Rosen (EPR) paradox and Bell’s failure of local-hiddenvariable (LHV) theories are three historically famous forms of “quantum nonlocality”. We give experimental criteria for these three forms of nonlocality in multi-particle systems, with the aim of better understanding the transition from microscopic to macroscopic nonlocality. We examine the nonlocality of N separated spin J systems. First, we obtain multipartite Bell inequalities that address the correlation between spin values measured at each site, and then we review spin squeezing inequalities that address the degree of reduction in the variance of collective spins. The latter have been particularly useful as a tool for investigating entanglement in Bose–Einstein condensates (BEC). We present solutions for two topical quantum states: multi-qubit Greenberger–Horne–Zeilinger (GHZ) states, and the ground state of a two-well BEC.     

Inequality relations for the hierarchy of quantum correlations in two-qubit systems

Entanglement, quantum steering and Bell nonlocality can be used to describe the distinct quantum correlations of quantum systems. Because of their different characteristics and application fields, how to divide them quantitatively and accurately becomes particularly important. Based on the sufficient and necessary criterion for quantum steering of an arbitrary two-qubit T-state, we derive the inequality relations between quantum steering and entanglement as well as between quantum steering and Bell nonlocality for the T-state. Additionally, we have verified those relations experimentally.     

Multipartite quantum correlations among atoms in QED cavities

We study the nonlocality dynamics for two models of atoms in cavity quantum electrodynamics (QED); the first model contains atoms in a single cavity undergoing nearest-neighbor interactions with no initial correlation, and the second contains atoms confined in n different and noninteracting cavities, all of which were initially prepared in a maximally correlated state of n qubits corresponding to the atomic degrees of freedom. The nonlocality evolution of the states in the second model shows that the corresponding maximal violation of a multipartite Bell inequality exhibits revivals at precise times, defining, nonlocality sudden deaths and nonlocality sudden rebirths, in analogy with entanglement. These quantum correlations are provided analytically for the second model to make the study more thorough. Differences in the first model regarding whether the array of atoms inside the cavity is arranged in a periodic or open fashion are crucial to the generation or redistribution of quantum correlations. This contribution paves the way to using the nonlocality multipartite correlation measure for describing the collective complex behavior displayed by slightly interacting cavity QED arrays.     

Sharing quantum nonlocality in star network scenarios

The Bell nonlocality is closely related to the foundations of quantum physics and has significant applications to security questions in quantum key distributions. In recent years, the sharing ability of the Bell nonlocality has been extensively studied. The nonlocality of quantum network states is more complex. We first discuss the sharing ability of the simplest bilocality under unilateral or bilateral POVM measurements, and show that the nonlocality sharing ability of network quantum states under unilateral measurements is similar to the Bell nonlocality sharing ability, but different under bilateral measurements. For the star network scenarios, we present for the first time comprehensive results on the nonlocality sharing properties of quantum network states, for which the quantum nonlocality of the network quantum states has a stronger sharing ability than the Bell nonlocality.     

Monogamy relations of nonclassical correlations for multi-qubit states

Nonclassical correlations have been found useful in many quantum information processing tasks, and various measures have been proposed to quantify these correlations. In this work, we mainly study one of nonclassical correlations, called measurement-induced nonlocality (MIN). First, we establish a close connection between this nonlocal effect and the Bell nonlocality for two-qubit states. Then, we derive a tight monogamy relation of MIN for any pure three-qubit state and provide an alternative way to obtain similar monogamy relations for other nonclassical correlation measures, including squared negativity, quantum discord, and geometric quantum discord. Finally, we find that the tight monogamy relation of MIN is violated by some mixed three-qubit states, however, a weaker monogamy relation of MIN for mixed states and even multi-qubit states is still obtained.     

Enhancing non-local correlations in the bipartite partitions of two qubit-system with non-mutual interaction

Several quantum-mechanical correlations, notably, quantum entanglement, measurement-induced nonlocality and Bell nonlocality are studied for a two qubit-system having no mutual interaction. Analytical expressions for the measures of these quantum-mechanical correlations of different bipartite partitions of the system are obtained, for initially two entangled qubits and the two photons are in their vacuum states. It is found that the qubits-fields interaction leads to the loss and gain of the initial quantum correlations. The lost initial quantum correlations transfer from the qubits to the cavity fields. It is found that the maximal violation of Bell’s inequality is occurring when the quantum correlations of both the logarithmic negativity and measurement-induced nonlocality reach particular values. The maximal violation of Bell’s inequality occurs only for certain bipartite partitions of the system. The frequency detuning leads to quick oscillations of the quantum correlations and inhibits their transfer from the qubits to the cavity modes. It is also found that the dynamical behavior of the quantum correlation clearly depends on the qubit distribution angle.     

Simplified Scheme for Test of Quantum Nonlocality Without Using Bell Inequality

A simplified scheme is proposed for the test of quantum nonlocality of the type described by Hardy [Phys.Rev.Left.71 (1993) 1665].In the scheme two appropriately prepared atoms are simultaneously sent through a cavity and dispersively interact with the cavity field.Then state-selective measurements are performed on these atoms,which may reveal quantum nonlocality without using Bell inequality.We also propose a simple scheme for the generation of multi-atom entangled states.``     

Simplified Scheme for Test of Quantum Nonlocality Without Using Bell Inequality

A simplified scheme is proposed for the test of quantum nonlocality of the type described by Hardy [Phys.Rev.Left.71 (1993) 1665] .In the scheme two appropriately prepared atoms are simultaneously sent through a cavity and dispersively interact with the cavity field.Then state-selective measurements are performed on these atoms,which may reveal quantum nonlocality without using Bell inequality.We also propose a simple scheme for the generation of multi-atom entangled states.     

基于量子相干性的四体贝尔不等式构建

贝尔不等式在定域性和实在性的双重假设下,对于被分隔的粒子同时被测量时其结果的可能关联程度建立了一个严格的限制,违反贝尔不等式确保量子态存在纠缠.本文利用量子相干性的l1和相对熵测度构建了四体量子贝尔不等式,发现一般实系数Greenberger-Horne-Zeilinger纯态和簇纯态总是违反四体相对熵相干性测度贝尔不等式,因此违反四体相对熵相干性测度贝尔不等式的这些态是纠缠态.     

Quantum correlations in spin models

Bell nonlocality, entanglement and nonclassical correlations are different aspects of quantum correlations for a given state. There are many methods to measure nonclassical correlations. In this paper, nonclassical correlations in two-qubit spin models are measured by the use of measurement-induced disturbance (MID) [S. Luo, Phys. Rev. A 77 (2008) 022301] and geometric measure of quantum discord (GQD) [B. Daki?, V. Vedral, C. Brukner, Phys. Rev. Lett. 105 (2010) 190502]. Their dependences on external magnetic field, spin–spin coupling, and the Dzyaloshinskii–Moriya (DM) interaction are presented in detail. We also compare Bell nonlocality, entanglement measured by concurrence, MID and GQD and illustrate their different characteristics.     

Testing the structure of multipartite entanglement with Bell inequalities

We show that the rich structure of multipartite entanglement can be tested following a device-independent approach. Specifically we present Bell inequalities for distinguishing between different types of multipartite entanglement, without placing any assumptions on the measurement devices used in the protocol, in contrast with usual entanglement witnesses. We first address the case of three qubits and present Bell inequalities that can be violated by W states but not by Greenberger-Horne-Zeilinger states, and vice versa. Next, we devise 'subcorrelation Bell inequalities' for any number of parties, which can provably not be violated by a broad class of multipartite entangled states (generalizations of Greenberger-Horne-Zeilinger states), but for which violations can be obtained for W states. Our results give insight into the nonlocality of W states. The simplicity and robustness of our tests make them appealing for experiments.     

The Essence of More Nonlocality with Less Entanglement in Bell Tests

In this paper, we will explore the essence of the phenomenon that state with less entanglement may generate greater Bell violation in the two-qubit Bell tests with CH-type inequalities, i.e., more nonlocality with less entanglement. We will show that this interesting but counterintuitive phenomenon is caused by the rotational asymmetry of the nonmaximally entangled state in the measurement plane. This asymmetry allows the both-side detection probabilities and the one-side detection probabilities obtain their maximal values with nonmaximally entangled state. But the maximal Bell violation may not always happen on nonmaximally entangled state, because these probabilities will compete with each other, and the Bell violation behaves differently for various CH-type inequalities.     

三光子GHZ态中不同Bell型不等式的实验研究

实验研究了Bell不等式、Mermin不等式和Svetlichny不等式在GHZ态中对定域实在论结果的破坏. 采用目标态密度矩阵的方法给出了实验制备的GHZ态的保真度, 得到了三个不等式在GHZ态中的测量值. 实验结果表明, 三个Bell型不等式在同一个状态下对定域实在论结果破坏程度不同, 在量子密钥分配中可以选择合适的非定域性描述方式考察所用信道的安全性.     

Einstein-Podolsky-Rosen Steering for Mixed Entangled Coherent States

By using the Born Markovian master equation, we study the relationship among the Einstein–Podolsky–Rosen (EPR) steering, Bell nonlocality, and quantum entanglement of entangled coherent states (ECSs) under decoherence. We illustrate the dynamical behavior of the three types of correlations for various optical field strength regimes. In general, we find that correlation measurements begin at their maximum and decline over time. We find that quantum steering and nonlocality behave similarly in terms of photon number during dynamics. Furthermore, we discover that ECSs with steerability can violate the Bell inequality, and that not every ECS with Bell nonlocality is steerable. In the current work, without the memory stored in the environment, some of the initial states with maximal values of quantum steering, Bell nonlocality, and entanglement can provide a delayed loss of that value during temporal evolution, which is of interest to the current study.     

Dynamical nonlocality of the entangled coherent state in the phase damping model

This paper studies the dynamics of nonlocality for a bosonic entangled coherent state in a phase damping model. The density operator of the system is solved by using a superoperator method. The dynamics of nonlocality for the bosonic entangled coherent state is uncovered by the Bell operator based on the pseudospin operator of a light field. The dynamics of the nonlocality for this state has also been studied by other Bell operators. The result of the numerical calculations of the Bell function shows that the quantum nonlocality heavily depends on the chosen Bell operator.     

Detecting genuine multipartite quantum nonlocality: a simple approach and generalization to arbitrary dimensions

The structure of Bell-type inequalities detecting genuine multipartite nonlocality, and hence detecting genuine multipartite entanglement, is investigated. We first present a simple and intuitive approach to Svetlichny's original inequality, which provides a clear understanding of its structure and of its violation in quantum mechanics. Based on this approach, we then derive a family of Bell-type inequalities for detecting genuine multipartite nonlocality in scenarios involving an arbitrary number of parties and systems of arbitrary dimension. Finally, we discuss the tightness and quantum mechanical violations of these inequalities.     

Quantum entanglement and quantum nonlocality for N-photon entangled states

Quantum entanglement and quantum nonlocality of N-photon entangled states |\psi_{N m}\rangle =C_m[\cos\gamma|N-m\rangle₁|m\rangle₂ +\e^{\i\θ_m}\sin\gamma|m\rangle₁|N-m\rangle₂] and their superpositions are studied. We point out that the relative phase θ_m affects the quantum nonlocality but not the quantum entanglement for the state |\psi_{N m}\rangle. We show that quantum nonlocality can be controlled and manipulated by adjusting the state parameters of |\psi_{N m}\rangle, superposition coefficients, and the azimuthal angles of the Bell operator. We also show that the violation of the Bell inequality can reach its maximal value under certain conditions. It is found that quantum superpositions based on |\psi_{N m}\rangle can increase the amount of entanglement, and give more ways to reach the maximal violation of the Bell inequality.     

Optimal Quantum Violations of n-Locality Inequalities with Conditional Dependence on Inputs

Bell experiment in a network gives rise to a form of quantum nonlocality which is conceptually different from traditional multipartite Bell nonlocality. In this work, the star-network configuration involving arbitrary n independent sources and $(n+1)$ parties, including n edge parties and one central party is considered. Each of the n edge parties shares a physical system with the central party. Each edge party receives $2^{m-1}$ number of inputs, and the central party receives an arbitrary m number of inputs. The conditional dependence on the inputs of each edge party is imposed so that the local probabilities satisfy a set of constraints. A family of generalized n-locality inequalities is proposed in the arbitrary input scenario by imposing the set of constraints on inputs. The optimal quantum violation of the inequalities is derived by using an elegant sum-of-squares approach without specifying the dimension of the quantum system. Notably, the optimal quantum value is achieved only when the set of linear constraints on inputs is satisfied, which, in turn, self-tests the observables required for each edge party. It shows that while conditional dependence on inputs significantly reduces the n-local bound of the inequalities, the optimal quantum violation remains invariant. It argues that this implies a more robust test of network non-locality, which can be revealed for smaller visibility parameters of the corresponding state. Further, the network nonlocality is characterized and examine its correspondence with suitably derived standard Bell nonlocality.