Nonclassicality of a two-variable Hermite polynomial state

The nonclassicality of the two-variable Hermite polynomial state is investigated. It is found that the two-variable Hermite polynomial state can be considered as a two-mode photon subtracted squeezed vacuum state. A compact expression for the Wigner function is also derived analytically by using the Weyl-ordered operator invariance under similar transformations. Especially, the nonclassicality is discussed in terms of the negativity of the Wigner function. Then violations of Bell’s inequality for the two-variable Hermite polynomial state are studied.     

Nonlocality of Two-Qubit and Three-Qubit Schmidt-Correlated States

We investigate the nonlocality of Schmidt-correlated (SC) states, and present analytical expressions of the maximum violation value of Bell inequalities. It is shown that the violation of Clauser-Horne-Shimony-Holt (CHSH) inequality is necessary and sufficient for the nonlocality of two-qubit SC states, whereas the violation of the Svetlichny inequality is only a sufficient condition for the genuine nonlocality of three-qubit SC states. Furthermore, the relations among the maximum violation values, concurrence, and relative entropy entanglement are discussed.     

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.     

三比特类GHZ态的Bell型不等式和非定域性

研究了一般形式类GHZ(Greenberger-Horne-Zeilinger)态的共生纠缠度及非定域性, 给出了类GHZ纠缠态的共生纠缠、Mermin不等式和Svetlichny不等式的解析表达式, 并通过数值计算讨论纠缠与非定域性之间的关系. 结果表明, 类GHZ纠缠态的共生纠缠和两个Bell型不等式描述的非定域性是一致的, Bell算符及其参量, 能够明显展示量子态的非定域特性. 关键词： 量子信息 类GHZ态 共生纠缠 Bell型不等式     

Quantum Measurement of Two-Qubit System in Damping Noise Environment

It is known that the inevitable interaction of the entangled qubits with their environments may result in the degradation of quantum correlation.We study the decoherence of two remote qubits under general local single-and two-sided amplitude-damping channel(ADC).By using concurrence,quantum discord and Clauser-Horne-ShimonyHolt(CHSH)inequality,we find that the relation between the residual quantum correlations and the initial ones are different.Recently,Wang et al.[Int.J.Theor.Phys.54(2015)5]showed that there exist a set of partially entangled states that are more robust than maximally entangled states in terms of the residual quantum correlation measured by concurrence,fully entangled fraction and quantum discord,respectively.Here we find that both in single-and two-sided ADC,only the evolution of CHSH inequality with the initial parameter is proportional to that of the initial nonlocality.That means the initial state with maximally nonlocality will retain its role in the evolution.It implies that the evolution of nonlocality may reveal the characteristics of quantum state better.Furthermore,we discuss the evolutions of the three different quantum measurements with the initial parameter under generalized amplitude damping channel(GADC)and find that they are all proportional to that of the initial state.     

等距离耦合腔系统中的非局域性

本文研究的物理系统由3个二能级原子和3个等距离单模腔构成. 3个单模腔分别处于等边三角形的3个顶点, 腔与腔之间通过光纤耦合. 采用Mermin-Ardehali-Belinksii-Klyshko不等式(简称MABK不等式)表征三体量子态的非局域性. 本文利用数值计算方法, 研究了原子初态或腔场初态为W态情况下三体系统量子态的MABK不等式违背, 讨论了腔模与光纤模间的耦合系数变化对MABK不等式违背的影响. 计算结果表明: 三原子量子态和三腔场量子态均呈现出MABK不等式违背, 并且随腔模与光纤模间耦合系数增大, 三原子量子态的非局域性增强.     

Fully nonlocal, monogamous, and random genuinely multipartite quantum correlations

Local measurements on bipartite maximally entangled states can yield correlations that are maximally nonlocal, monogamous, and with fully random outcomes. This makes these states ideal for bipartite cryptographic tasks. Genuine-multipartite nonlocality constitutes a stronger notion of nonlocality in the multipartite case. Maximal genuine-multipartite nonlocality, monogamy, and random outcomes are thus highly desired properties for genuine-multipartite cryptographic scenarios. We prove that local measurements on any Greenberger-Horne-Zeilinger state can produce correlations that are fully genuine-multipartite nonlocal, monogamous, and with fully random outcomes. A key ingredient in our proof is a multipartite chained Bell inequality detecting genuine-multipartite nonlocality, which we introduce. Finally, we discuss applications to device-independent secret sharing.     

Testing the nonlocality of entangled states by a new Bell-like inequality

We test a new four-qubit entangled state by the former Bell-like inequalities and find that it violates these inequalities, but not maximally. According to this entangled state, we build a new Bell-like inequality, which is violated by this new state maximally. We also determine the nonlocality of some other four-qubit states by the new inequality. It is found that the new inequality acts as a strong entanglement witness for the new state. This can be used to test new entangled states experimentally.     

Entanglement and nonlocality of one- and two-mode combination squeezed state

We investigate the entanglement and nonlocality properties of one- and two-mode combination squeezed vacuum state (OTCSS, with two-parameter λ and γ) by analyzing the logarithmic negativity and the Bell's inequality. It is found that this state exhibits larger entanglement than that of the usual two-mode squeezed vacuum state (TSVS), and that in a certain regime of λ, the violation of Bell's inequality becomes more obvious, which indicates that the nonlocality of OTCSS can be stronger than that of TSVS. As an application of OTCSS, the quantum teleportation is examined, which shows that there is a region spanned by λ and γin which the fidelity of OTCSS channel is larger than that of TSVS.     

Violation of the Mermin-Ardehali-Belinksii-Klyshko Inequality of Three Coupled Atoms Interacting with a Cavity

In this paper we study the nonlocality evolution for three identical two-level atoms, each coupled with the others and interacted with a single-mode cavity which is initially in a superposition of the vacuum and one-photon states. The nonlocality is characterized by violation of the Mermin-Ardehali-Belinksii-Klyshko (MABK) inequality. The influences of atom-atom coupling constant and the initial state of the cavity field on violation of the MABK inequality are discussed. The results obtained by numerical simulation show that the MABK parameter decreases as the ratio of the atom-atom coupling to the atom-cavity coupling increases, and that it increases with the initial population of the one-photon state.     

Cavity-loss-induced Bell-nonlocality sudden death in the Tavis-Cummings model

The tripartite nonlocality is measured by the extent of violation of multipartite Bell inequality in Tavis-Cummings model with cavity loss. The effect of Bell-nonlocality sudden death is demonstrated. It is important that the study of tripartite system can exhibit fundamental characteristics which do not exist in bipartite systems.     

Revealing hidden Einstein-Podolsky-Rosen nonlocality

Steering is a form of quantum nonlocality that is intimately related to the famous Einstein-Podolsky-Rosen (EPR) paradox that ignited the ongoing discussion of quantum correlations. Within the hierarchy of nonlocal correlations appearing in nature, EPR steering occupies an intermediate position between Bell nonlocality and entanglement. In continuous variable systems, EPR steering correlations have been observed by violation of Reid's EPR inequality, which is based on inferred variances of complementary observables. Here we propose and experimentally test a new criterion based on entropy functions, and show that it is more powerful than the variance inequality for identifying EPR steering. Using the entropic criterion our experimental results show EPR steering, while the variance criterion does not. Our results open up the possibility of observing this type of nonlocality in a wider variety of quantum states.     

Experimentally faking the violation of Bell's inequalities

Entanglement witnesses such as Bell inequalities are frequently used to prove the nonclassicality of a light source and its suitability for further tasks. By demonstrating Bell inequality violations using classical light in common experimental arrangements, we highlight why strict locality and efficiency conditions are not optional, particularly in security-related scenarios.     

The collapse and revival of Bell-nonlocality of two macroscopic fields interacting with resonant atoms

We investigate the nonlocality dynamics of two initially entangled macroscopic fields each interacting with a resonant two-level atom. The nonlocality of macroscopic field is characterized by the extent to which the Bell Clauser-Horne-Shimony-Holt (CHSH)'s inequality for continuous-variable states is violated. We show that the collapse and revival of the Bell-nonlocality are similar to the collapse and revival of the atomic population inversion of the Jaynes-Cummings model (JCM).     

Experimental tests of bell inequalities. Are all local models really excluded?

Bell inequality tests performed by atomic cascade experiments always make use of a coincidence counting electronics. It is shown that such electronics can act as a “source of nonlocality” in the correlation function, even if every phenomenon involved is perfectly local. A simple example illustrating this situation is given.     

Connecting Quantum Contextuality and Genuine Multipartite Nonlocality with the Quantumness Witness

The Clauser-Horne-Shimony-Holt-type noncontextuality inequality and the Svetlichny inequality are derived from the Alicki-van Ryn quantumness witness.Thus connections between quantumness and quantum contextuality,and between quantumness and genuine multipartite nonlocality are established.     

广义GHZ态的纠缠与非定域性

对GHZ态与W态叠加的三粒子广义GHZ态,用Svetlichny不等式,给出了其非定域性的解析表达式.用数值计算方法讨论了纠缠与非定域性之间的关系. 关键词： 广义GHZ态 剩余纠缠 Svetlichny不等式 非定域性     

Quantum nonlocality does not imply entanglement distillability

Entanglement and nonlocality are both fundamental aspects of quantum theory, and play a prominent role in quantum information science. The exact relation between entanglement and nonlocality is, however, still poorly understood. Here we make progress in this direction by showing that, contrary to what previous work suggested, quantum nonlocality does not imply entanglement distillability. Specifically, we present analytically a 3-qubit entangled state that is separable along any bipartition. This implies that no bipartite entanglement can be distilled from this state, which is thus fully bound entangled. Then we show that this state nevertheless violates a Bell inequality. Our result also disproves the multipartite version of a long-standing conjecture made by Peres.     

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.     

Nonlocality and Gleason's lemma. Part I. Deterministic theories

J. S. Bell's classic 1966 review paper on the foundations of quantum mechanics led directly to the Bell nonlocality theorem. It is not widely appreciated that the review paper contained the basic ingredients needed for a nonlocality result which holds in certain situations where the Bell inequality is not violated. We present in this paper a systematic formulation and evaluation of an argument due to Stairs in 1983, which establishes a nonlocality result based on the Bell-Kochen-Specker paradox in quantum mechanics.