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基于量子相干性的四体贝尔不等式构建

Four-partite Bell inequalities based on quantum coherence
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摘要 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. It is well known that Bell inequalities are derived under the assumptions of locality and realism. Bell inequalities impose strict constraints on the statistical correlations of measurements of multipartite systems. Violating each of them guarantees the existence of quantum correlations in a quantum state. A quantum state with non-vanishing entanglement may violate some Bell inequalities. Recent progress of the fields like quantum biology and quantum thermodynamics reveals a particular role of quantum coherence in quantum information processing. Quantum coherence is identified by the presence of off-diagonal terms in the density matrix. To quantify quantum coherence of a given state, Baumgratz et al.(Baumgratz T, Cramer M, Plenio M B 2014 Phys. Rev. Lett. 113 140401) provided several kinds of coherence measures such as l_1-norm of coherence and relative entropy of coherence. In this paper, we propose to use quantum coherence to derive Bell inequalities. We construct the Bell inequalities of four-partite product states with l_1-norm of coherence, relative entropy of coherence. In the Bell inequalities of four-partite correlations, measurement operators are products of local measurement operators. Each local operator is one of the two arbitrary observables. We consider the violations of the four-partite Bell inequalities by the four-partite general pure Greenberger-Horne-Zeilinger(GHZ) state,cluster states, W states with real coefficients. We also investigate the violations of the four-partite Bell inequalities by the four-partite GHZ class mixed states, cluster class mixed states, W class mixed states and Dicke class mixed states.It is shown that the four-partite Bell inequalities in terms of relative entropy of coherence are always violated by the four-partite general pure GHZ states, cluster states with the real coefficients. Hence there is non-vanishing entanglement for these states.
出处 《物理学报》 SCIE EI CAS CSCD 北大核心 2017年第20期10-17,共8页 Acta Physica Sinica
基金 国家自然科学基金(批准号:11375152)资助的课题~~
关键词 贝尔不等式 量子相干性 多体量子态 Bell inequalities, quantum coherence, multipartite quantum states
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