Bose-Hubbard模型中系统初态对量子关联的影响

量子关联是量子信息、量子计算与量子计量领域的重要资源, 在量子纠缠和贝尔非局域性中, 两子系统起着同等关键的作用, Einstein-Podolsky-Rosen (EPR)量子引导关联的强度介于量子纠缠和贝尔非局域性之间, 对单向EPR量子引导关联而言两子系统的作用不对等. 本文研究了双模Bose-Hubbard模型中模间量子关联的动态特性, 揭示了EPR量子引导关联的取向对系统初态模间交换对称性的依赖关系. 根据Hillery-Zubairy纠缠判据以及基于最大平均量子Fisher信息的纠缠判据考察了系统初态对模间量子纠缠演化规律的影响. 如果模间耦合强度远大于同一势阱内粒子间的相互作用, 初始处于SU(2)相干态的系统在具有确定的两子系统交换对称性的条件下, 其量子关联呈现简单的周期性演化规律; 当这种对称性破缺时, 模间量子关联的演化呈现较复杂的崩塌与回复现象.     

Bell-CHSH function approach to quantum phase transitions in matrix product systems

Recently, nonlocality and Bell inequalities have been used to investigate quantum phase transitions (QPTs) in low-dimensional quantum systems. Nonlocality can be detected by the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) function. In this work, we extend the study of the Bell-CHSH function (BCF) to QPTs in matrix product systems (MPSs). In these kinds of QPTs, the ground-state energy remains analytical in the vicinity of the QPT points, and they are usually called MPS-QPTs. For several typical models, our results show that the BCF can signal MPS-QPTs very well. In addition, we find the BCF can capture signal of QPTs in unentangled states and classical states, for which other measures of quantum correlation (quantum entanglement and quantum discord) fail. Furthermore, we find that in these MPSs, there exists some kind of quantum correlation which cannot be characterized by entanglement, or by nonlocality.     

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.     

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.     

Steering Witness and Steering Criterion of Gaussian States

Quantum steering is an important quantum resource, which is intermediate between entanglement and Bell nonlocality. In this paper, we study steering witnesses for Gaussian states in continuous-variable systems. We give a definition of steering witnesses by covariance matrices of Gaussian states, and then obtain a steering criterion by steering witnesses to detect steerability of any (m+n)-mode Gaussian states. In addition, the conditions for two steering witnesses to be comparable and the optimality of steering witnesses are also discussed.     

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     

Measurement-based entanglement purification for entangled coherent states

The entangled coherent states (ECSs) have been widely used to realize quantum information processing tasks. However, the ECSs may suffer from photon loss and decoherence due to the inherent noise in quantum channel, which may degrade the fidelity of ECSs. To overcome these obstacles, we present a measurement-based entanglement purification protocol (MBEPP) for ECSs to distill some highquality ECSs from a large number of low-quality copies. We first show the principle of this MBEPP without considering the photon loss. After that, we prove that this MBEPP is feasible to correct the error resulted from the photon loss. Additionally, this MBEPP only requires to operate the Bell state measurement without performing local two-qubit gates on the noisy pairs and the purified high-quality ECSs can be preserved for other applications. This MBEPP may have application potential in the implementation of long-distance quantum communication.     

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.     

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.     

A Note on Quantum Bell Nonlocality and Quantum Entanglement for High Dimensional Quantum Systems

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.

     

Quantum correlations in non-Markovian environments

We have studied the analytical Markovian and non-Markovian dynamics of quantum correlations, such as entanglement, quantum discord and Bell nonlocalities for three noisy qubits. Quantum correlation as measured by quantum discord is found to be immune to death contrary to entanglement and Bell nonlocality for initial GHZ- or W-type mixed states.     

Generalized Steering Robustness of Bipartite Quantum States

EPR steering is a kind of quantum correlation that is intermediate between entanglement and Bell nonlocality. In this paper, by recalling the definitions of unsteerability and steerability, some properties of them are given, e.g, it is proved that a local quantum channel transforms every unsteerable state into an unsteerable state. Second, a way of quantifying quantum steering, which we called the generalized steering robustness (GSR), is introduced and some interesting properties are established, including: (1) GSR of a state vanishes if and only if the state is unsteerable; (2) a local quantum channel does not increase GSR of any state; (3) GSR is invariant under each local unitary operation; (4) as a function on the state space, GSR is convex and lower-semi continuous. Lastly, by using the majorization between the reduced states of two pure states, GSR of the two pure states are compared, and it is proved that every maximally entangled state has the maximal GSR.     

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.     

Steering quantum nonlocalities of quantum dot system suffering from decoherence

The important applications of quantum dot system are to implement logic operations and achieve universal quantum computing based on different quantum nonlocalities. Here, we characterize the quantum steering, Bell nonlocality, and nonlocal advantage of quantum coherence (NAQC) of quantum dot system suffering nonunital and unital channels. The results reveal that quantum steering, Bell nonlocality, and NAQC can display the traits of dissipation, enhancement, and freezing. One can achieve the detections of quantum steering, Bell nonlocality, and NAQC of quantum dot system in different situations. Among these quantum nonlocalities, NAQC is the most fragile, and it is most easily influenced by different system parameters. Furthermore, considering quantum dot system coupling with amplitude damping channel and phase damping channel, these quantum nonlocalities degenerate with the enlargement of the channel parameters $t$ and $\varGamma$. Remarkably, measurement reversal can effectively control and enhance quantum steering, Bell nonlocality, and NAQC of quantum dot system suffering from decoherence, especially in the scenarios of the amplitude damping channel and strong operation strength.     

Entanglement dynamics and Bell violation of three-qubit states coupled to an XY spin chain with Dzyaloshinski–Moriya interaction

We investigate the entanglement dynamics and Bell violation of three-qubit quantum states under an environment consisting of an XY spin chain with Dzyaloshinski–Moriya (DM) interaction. From the results, we find that the entanglement dynamics depends not only on the DM interaction, the magnetic field, and the anisotropy parameter but also on the number of the freedom degrees of the environment. The decoherence-free subspaces of our model have been identified and the Bell violation of quantum states is also discussed.     

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.     

Robustness of entanglement for Bell decomposable states

We propose a simple geometrical approach for finding robustness of entanglement for Bell decomposable states of two-qubit quantum systems. It is shown that for these states robustness is equal to the concurrence. We also present an analytical expression for two separable states that wipe out all entanglement of these states. Random robustness of these states is also obtained. We also obtain robustness of a class of states obtained from Bell decomposable states via some special local operations and classical communications (LOCC).Received: 28 October 2002, Published online: 5 August 2003PACS: 03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)     

Randomness versus nonlocality and entanglement

The outcomes obtained in Bell tests involving two-outcome measurements on two subsystems can, in principle, generate up to 2?bits of randomness. However, the maximal violation of the Clauser-Horne-Shimony-Holt inequality guarantees the generation of only 1.23?bits of randomness. We prove here that quantum correlations with arbitrarily little nonlocality and states with arbitrarily little entanglement can be used to certify that close to the maximum of 2?bits of randomness are produced. Our results show that nonlocality, entanglement, and randomness are inequivalent quantities. They also imply that device-independent quantum key distribution with an optimal key generation rate is possible by using almost-local correlations and that device-independent randomness generation with an optimal rate is possible with almost-local correlations and with almost-unentangled states.     

Two-Mode Excited Entangled Coherent State: Nonclassicality and Entanglement

Two-mode excited entangled coherent states (TME-ECSs) are introduced by operating repeatedly the photon-excited operator on the ECSs. It is shown that the normalization constant is related to the product of two Laguerre polynomials. The influence of the operation on nonclassical behaviour of the ECSs is investigated in terms of cross-correlation function, anti-bunching effect and the negativity of Wigner function, which show that nonclassical properties can be enhanced. In addition, inseparability properties of the TME-ECSs are discussed by using Bell inequality and concurrence. It is found that the degree of quantum entanglement of even ECSs increases with the increase of the total excited photon number, and the violation of Bell inequality can be present for both even and odd case only when the total excited photon numbers are even and odd, respectively.     

Nonlocality in many-body quantum systems detected with two-body correlators

Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems, mostly because the available multipartite Bell inequalities involve high-order correlations among many particles, which are hard to access theoretically, and even harder experimentally. Standard, “theorist- and experimentalist-friendly” many-body observables involve correlations among only few (one, two, rarely three...) particles. Typically, there is no multipartite Bell inequality for this scenario based on such low-order correlations. Recently, however, we have succeeded in constructing multipartite Bell inequalities that involve two- and one-body correlations only, and showed how they revealed the nonlocality in many-body systems relevant for nuclear and atomic physics [Tura et al., Science 344 (2014) 1256]. With the present contribution we continue our work on this problem. On the one hand, we present a detailed derivation of the above Bell inequalities, pertaining to permutation symmetry among the involved parties. On the other hand, we present a couple of new results concerning such Bell inequalities. First, we characterize their tightness. We then discuss maximal quantum violations of these inequalities in the general case, and their scaling with the number of parties. Moreover, we provide new classes of two-body Bell inequalities which reveal nonlocality of the Dicke states—ground states of physically relevant and experimentally realizable Hamiltonians. Finally, we shortly discuss various scenarios for nonlocality detection in mesoscopic systems of trapped ions or atoms, and by atoms trapped in the vicinity of designed nanostructures.