Trade-off relations between measurement dependence and hiddenness for separable hidden variable models
Trade-off relations between measurement dependence and hiddenness for separable hidden variable models
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发表时间：
2022-08
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通讯作者：
Ryo Takakura;Kei Morisue;Issei Watanabe;G. Kimura
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作者：
Ryo Takakura;Kei Morisue;Issei Watanabe;G. Kimura
贝尔定理被研究为潜在隐变量模型假设之间的权衡关系。考虑到引入一组隐变量本身就是基本假设之一，我们引入了隐性的度量，即表示需要隐变量的程度的量。我们为可分离模型推导了新颖的松弛 Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) 不等式，这些模型是隐变量模型，在测量依赖性和隐藏性方面仅满足局部性而不满足测量独立性条件。导出的关系可以解释为 CHSH 场景中可分离模型的测量依赖性和隐藏性之间的权衡关系。还表明，该关系为通过可分离模型实现措施提供了充分必要条件。
The Bell theorem is investigated as a trade-off relation between assumptions for the underlying hidden variable model. Considering the introduction of a set of hidden variables itself to be one of the essential assumptions, we introduce a measure of hiddenness, a quantity that expresses the degree to which hidden variables are needed. We derive novel relaxed Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequalities for separable models, which are hidden variable models that only satisfy the locality but not the measurement independence condition, in terms of their measurement dependence and hiddenness. The derived relations can be interpreted as trade-off relations between the measurement dependence and hiddenness for separable models in the CHSH scenario. It is also revealed that the relation gives a necessary and sufficient condition for the measures to be realized by a separable model.