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On Distinguishing of Non-Signaling Boxes via Completely Locality Preserving Operations

机译：通过完全保留位置来区分非信号箱

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摘要

We introduce a scenario of discrimination between bipartite boxes and apply it to boxes with two binary inputs and two binary outputs ( ). We develop the analogy between the theory of Bell non-locality and the theory of entanglement by considering the class of completely locality preserving (CLP) operations. A CLP operation satisfies two conditions: 1) transforms boxes with local hidden variable model (LHVM) into boxes with LHVM (i.e., is locality preserving) and 2) when tensored with an identity operation, forms a new operation, which is also locality preserving. We derive linear program, which gives an upper bound on the probability of success of discrimination between different isotropic boxes using this class of operations. In particular, we provide an upper bound on the probability of success of discrimination between isotropic boxes with the same mixing parameter. As a counterpart of entanglement monotone, we use the non-locality cost. Discrimination is restricted by the fact that non-locality cost does not increase under considered class of operations and geometry of boxes. We provide an example of CLP operations, which are called comparing operations (COP). The latter operations consist of direct measurement of the shared box by both the parties, followed by a predefined strategy in order to establish the guess, which may depend on the obtained outcomes. We then show that with the help of the COP operations, one can distinguish perfectly any two extremal boxes in case and any local extremal box from any other extremal box in case of two inputs and two outputs of arbitrary cardinalities.
机译：我们介绍了二分框之间的区分方案，并将其应用于具有两个二进制输入和两个二进制输出的框。通过考虑完全局部性保留（CLP）操作的类，我们开发了Bell非局部性理论和纠缠理论之间的类比。 CLP操作满足两个条件：1）将具有局部隐藏变量模型（LHVM）的框转换为具有LHVM的框（即，保留局部性），以及2）当通过标识操作张量时，形成新的操作，该操作也保留局部性。我们推导了线性程序，该程序给出了使用此类操作成功区分不同各向同性盒的概率的上限。特别是，我们为具有相同混合参数的各向同性盒之间的成功识别概率提供了一个上限。作为纠缠单调的对应项，我们使用非局部成本。在考虑的操作类别和盒子几何形状下，非本地化成本不会增加的事实限制了歧视。我们提供了CLP操作的示例，称为比较操作（COP）。后者的操作包括双方直接测量共享框，然后执行预定策略以建立猜测，这可能取决于获得的结果。然后，我们证明，借助COP操作，可以完美区分两个情况下的任意两个极端盒和任意两个基数和两个任意基数的情况下的任何其他极端盒。

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