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.     

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.     

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     

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.     

Nonlocality and entanglement via the Unruh effect

Modeling the qubit by a two-level semiclassical detector coupled to a massless scalar field, we investigate how the Unruh effect affects the nonlocality and entanglement of two-qubit and three-qubit states when one of the entangled qubits is accelerated. Two distinct differences with the results of free field model in non-inertial frames are (i) for the two-qubit state, the CHSH inequality cannot be violated for sufficiently large but finite acceleration, furthermore, the concurrence will experience “sudden death”; and (ii) for the three-qubit state, not only does the entanglement vanish in the infinite acceleration limit, but also the Svetlichny inequality cannot be violated in the case of large acceleration.     

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.     

Concentration Effect of Quantum and Classical Correlations during Quantum Brachistochrone Evolution

We explore the role of quantum brachistochrone evolution to quantum and classical correlations in three-qubit systems, and show that the time-averaged correlations of three-qubit systems exhibit an obvious concentration effect, which means both the standard deviations of time-averaged quantum and classical correlations decrease with the separation angle. Furthermore, we find that the concentration effect on genuine tripartite entanglement is the most significant during the quantum brachistochrone evolution of three-qubit systems.     

Correlations Existing in Three-Qubit Product States

Analytic results of the relationship between local noncommutativity and non-violations of Svetlichny inequalities for three-qubit separable states are obtained. It is shown that the converse trade-off relations presented by Seevinck and Uffinck [Phys. Rev. A 2007 76 042105] do not always hold for three-qubit states, and that there exists some correlation even though the state is the simple product state.     

Symmetric extensions of quantum States and local hidden variable theories

While all bipartite pure entangled states violate some Bell inequality, the relationship between entanglement and nonlocality for mixed quantum states is not well understood. We introduce a simple and efficient algorithmic approach for the problem of constructing local hidden variable theories for quantum states. The method is based on constructing a so-called symmetric quasiextension of the quantum state that gives rise to a local hidden variable model with a certain number of settings for the observers Alice and Bob.     

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.     

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.     

Is the Devil in h?

This note is a part of my effort to rid quantum mechanics (QM) nonlocality. Quantum nonlocality is a two faced Janus: one face is a genuine quantum mechanical nonlocality (defined by the Lüders’ projection postulate). Another face is the nonlocality of the hidden variables model that was invented by Bell. This paper is devoted the deconstruction of the latter. The main casualty of Bell’s model is that it straightforwardly contradicts Heisenberg’s uncertainty and Bohr’s complementarity principles generally. Thus, we do not criticize the derivation or interpretation of the Bell inequality (as was done by numerous authors). Our critique is directed against the model as such. The original Einstein-Podolsky-Rosen (EPR) argument assumed the Heisenberg’s principle without questioning its validity. Hence, the arguments of EPR and Bell differ crucially, and it is necessary to establish the physical ground of the aforementioned principles. This is the quantum postulate: the existence of an indivisible quantum of action given by the Planck constant. Bell’s approach with hidden variables implicitly implies rejection of the quantum postulate, since the latter is the basis of the reference principles.     

Dynamics of Genuine Three-Qubit Entanglement in Ising Spin Systems

We investigate the dynamics of genuine three-qubit entanglement in the Ising model of three spins. A scheme is presented for generating the genuine three-qubit entanglement by the nearest-neighbour couplings. The effect of magnetic fields on the dynamics of genuine three-qubit entanglement is also discussed.     

Quantum state sharing of an arbitrary three-qubit state by using four sets of W-class states

A new application of the W-class state is investigated for quantum state sharing (QSTS) of an arbitrary three-qubit state. We demonstrate that four sets of W-class states can be used to realize the deterministic QSTS of an arbitrary three-qubit state based on the three-qubit von Neumann measurements and the local unitary operations. Our scheme considered here is secure against certain eavesdropping attacks.     

Entanglement Preserving in Quantum Copying of Three-Qubit Entangled State

We study the degree to which quantum entanglement survives when a three-qubit entangled state iscopied by using local and non-local processes, respectively, and investigate iterating quantum copyingfor the three-qubitsystem. There may exist inter-three-qubit entanglement and inter-two-qubit entanglement for the three-qubit system.We show that both local and non-local copying processes degrade quantum entanglement in the three-particle systemdue to a residual correlation between the copied output and the copying machine. We also show that the inter-two-qubitentanglement is preserved better than the inter-three-qubit entanglement in the local cloning process. We find thatnon-local cloning is much more efficient than the local copying for broadcasting entanglement, and output state vianon-local cloning exhibits the fidelity better than local cloning.     

Experimental entanglement distillation of two-qubit mixed states under local operations

We experimentally demonstrate optimal entanglement distillation from two forms of two-qubit mixed states under local filtering operations according to the constructive method introduced by [F. Verstraete, Phys. Rev. A 64, 010101(R) (2001)10.1103/PhysRevA.64.010101]. In principle, our setup can be easily applied to distilling entanglement from arbitrary two-qubit partially mixed states. We also test the violation of the Clauser-Horne-Shinmony-Holt inequality for the distilled state from the first form of mixed state to show its "hidden nonlocality."     

The Violation of Bell Inequalities in the Macroworld

We show that Bell inequalities can be violated in the macroscopic world. The macroworld violation is illustrated using an example involving connected vessels of water. We show that whether the violation of inequalities occurs in the microworld or the macroworld, it is the identification of nonidentical events that plays a crucial role. Specifically, we prove that if nonidentical events are consistently differentiated, Bell-type Pitowsky inequalities are no longer violated, even for Bohm's example of two entangled spin 1/2 quantum particles. We show how Bell inequalities can be violated in cognition, specifically in the relationship between abstract concepts and specific instances of these concepts. This supports the hypothesis that genuine quantum structure exists in the mind. We introduce a model where the amount of nonlocality and the degree of quantum uncertainty are parameterized, and demonstrate that increasing nonlocality increases the degree of violation, while increasing quantum uncertainty decreases the degree of violation.     

The incompatibility between local hidden variable theories and the fundamental conservation laws

I discuss in detail the result that the Bell’s inequalities derived in the context of local hidden variable theories for discrete quantized observables can be satisfied only if a fundamental conservation law is violated on the average. This result shows that such theories are physically nonviable, and makes the demarcating criteria of the Bell’s inequalities redundant. I show that a unique correlation function can be derived from the validity of the conservation law alone and this coincides with the quantum mechanical correlation function. Thus, any theory with a different correlation function, like any local hidden variable theory, is incompatible with the fundamental conservation laws and space-time symmetries. The results are discussed in the context of two-particle singlet and triplet states, GHZ states, and two-particle double slit interferometry. Some observations on quantum entropy, entanglement, and nonlocality are also discussed.     

Non-Markovian Effects on Bell-Nonlocality Sudden Death in Tripartite

The Bell-nonlocal behavior of three-qubit systems is studied in this paper. The three qubits without mutual interaction are independently coupled to different two band non-Markovian environments. We find that certain non-Markovian effect protects the nonlocality in short time scale, while on long time scale it leads to the Bell-nonlocality sudden death (BNSD).