The effect on (2, N, 2) Bell tests with distributed measurement dependence
The effect on (2, N, 2) Bell tests with distributed measurement dependence
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对具有分布式测量依赖性的 (2, N, 2) Bell 测试的影响
DOI：
10.1007/s11128-020-02819-x
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发表时间：
2020
影响因子：
2.5
通讯作者：
Ma Yan
中科院分区：
文献类型：
--
作者：
Li Dan-Dan;Chen Lin-Yan;Cao Ya;Huang Xiao-Hong;Gao Fei;Ma Yan
贝尔检验作为检测二部系统非局部性的原始工具，依赖于一个假设，即测量独立性。在实践中，很难保证测量的独立性。有必要研究放松测量独立性对贝尔测试的影响。在最简单的(2，2，2)CHSH Bell检验中，给出了CHSH相关函数的最大值与分布测量相关性(DMD)之间的关系，其中DMD是放松测量独立性的一般度量。然而，在每一方任意数量的测量的一般Bell场景中，即(2，N，2)，相关结果仍然缺失。为了解决这个问题，我们建立了保持局部性的(2，N，2)Pearle-Braunstein-Caves(PBC)链关联函数的最大值与DMD程度之间的关系，称为DMD诱导的PBC链不等式。此外，我们通过构造伪上界的局部隐变量模型来证明这些导出的不等式的紧性。与最简单的CHSH-Bell检验相比，我们推导的不等式需要更少的测量依赖量来伪造随N增加的量子预测，这有利于分析诸如随机性扩展等与设备无关的量子信息处理任务的安全性。
Bell tests, as primitive tools to detect nonlocality in bipartite systems, rely on an assumption, i.e., measurement independence. In practice, it is difficult to ensure measurement independence. It is necessary to investigate how Bell tests are affected by relaxing measurement independence. In the simplest (2, 2, 2) CHSH Bell test which consists of two parties, two measurements per party and two possible outcomes per measurement, the results between the maximal value of CHSH correlation function and distributed measurement dependence (DMD) are given, where DMD is a general measure of relaxing measurement independence. However, in a general Bell scenario of an arbitrary number of measurements per party, i.e., (2, N , 2), pertinent results are still missing. To solve it, we establish the relations between the maximal value of (2, N , 2) Pearle–Braunstein–Caves (PBC) chain correlation function that maintains the locality and the degree of DMD, denoted as DMD-induced PBC chain inequalities. Furthermore, we show the tightness of these derived inequalities via constructing local hidden variable models that fake the upper bounds. Compared with the simplest CHSH Bell test, our derived inequalities need less amount of measurement dependence to fake the quantum prediction with N increasing, which is beneficial to analyze the security of device-independent quantum information processing tasks such as randomness expansion.