Quantifying non-classical and beyond-quantum correlations in the unified operator formalism
Quantifying non-classical and beyond-quantum correlations in the unified operator formalism
复制标题
量化统一算子形式中的非经典和超量子相关性
DOI：
10.1088/1751-8113/47/42/424030
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
M. Piani
中科院分区：
文献类型：
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作者：
J. Geller;M. Piani
Acin et al . (2010；Rev. Lett. 104 140404)介绍了研究无信号关联的统一框架。这样的框架是基于局部量子测量的概念，但是，为了解释超量子相关性，允许非正半确定的全局伪态。在对形式主义的简短回顾之后，我们考虑它在一般非局部和超量子相关的量化中的使用。我们认为，统一的相关性框架为这种量化提供了一种简单的方法，特别是当量化意味着在资源理论场景中具有可操作性和有意义时，即，当考虑通过非资源处理资源时。我们在（伪）状态和抽象概率分布的水平上介绍了相关性鲁棒性的不同概念，特别关注相关性和伪状态的超量子鲁棒性。我们回顾了已知的结果，并认为，在统一的框架内，两个层次之间的关系——算子和概率分布——是非常严格的。我们指出在两个层次上对鲁棒性的考虑如何导致以与设备无关的方式量化纠缠的自然框架。最后，我们证明了实现超量子相关所需的非正算子的超量子鲁棒性与它们的负性和它们与量子态集的距离一致。作为一个例子，我们计算了噪声波佩斯库-罗利希盒的超量子鲁棒性。这篇文章是《物理杂志a：数学与理论》专刊的一部分，专门讨论“贝尔定理50年”。
Acin et al (2010 Phys. Rev. Lett. 104 140404) introduced a unified framework for the study of no-signalling correlations. Such a framework is based on the notion of local quantum measurements, but, in order to account for beyond-quantum correlations, global pseudo-states that are not positive semidefinite are allowed. After a short review of the formalism, we consider its use in the quantification of both general non-local and beyond-quantum correlations. We argue that the unified framework for correlations provides a simple approach to such a quantification, in particular when the quantification is meant to be operational and meaningful in a resource-theory scenario, i.e., when considering the processing of resources by means of non-resources. We relate different notions of robustness of correlations, both at the level of (pseudo-)states and abstract probability distributions, with particular focus on the beyond-quantum robustness of correlations and pseudo-states. We revisit known results and argue that, within the unified framework, the relation between the two levels—that of operators and that of probability distributions—is very strict. We point out how the consideration of robustness at the two levels leads to a natural framework for the quantification of entanglement in a device-independent way. Finally, we show that the beyond-quantum robustness of the non-positive operators needed to achieve beyond-quantum correlations coincides with their negativity and their distance from the set of quantum states. As an example, we calculate the beyond-quantum robustness for the case of a noisy Popescu–Rohrlich box. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’.