Operational foundations for complementarity and uncertainty relations
Operational foundations for complementarity and uncertainty relations
复制标题
互补性和不确定性关系的操作基础
DOI：
10.1103/physreva.101.052104
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发表时间：
2018
影响因子：
2.9
通讯作者：
R. Horodecki
中科院分区：
文献类型：
--
作者：
Debashis Saha;Michał Oszmaniec;L. Czekaj;Michał Horodecki;R. Horodecki
在量子世界中出现的所谓准备不确定性可以用纯操作术语来很好地理解，它在任何给定理论中的存在，也许不同于量子力学，可以通过检查测量统计来验证。也就是说，当对于某对可观测量来说，没有任何准备能够同时展示出它们的确定性统计时，在某个理论中就出现了不确定性。然而，如果我们不坚持不确定关系的右边只是给定理论左边的最小值，那么右边就不再是可操作的了。例如，在量子力学中，它是两个必须在量子形式主义中计算的可观测量的函数。此外，虽然可观测量的联合不可测性是一个操作概念，但玻尔意义上的互补性（即，就描述系统所需的信息而言）尚未以纯粹的操作术语表达。在此，我们提出了一个总的业务框架，为上述问题提供答案。我们引入了互补性的操作定义，并进一步假设互补观测量必须表现出不确定性，这意味着我们建议把（操作）互补性作为不确定性关系的右侧。特别是，我们确定了两个不同的概念的不确定性和互补性，上述原则在量子力学领域。我们还介绍了不确定性和互补性的一般措施的假设。为了定义互补性的量词，我们首先转向简单的独立性概念，它仅根据两个观测量的统计来定义。重要的是，对于干净的和极端的可观察性-即，那些不能被其他可观测量不可约地模拟的-任何独立性的度量都可约化为适当的互补度量。最后，作为我们的一般框架的应用程序，我们定义了一些互补性指标，并表明它们可以用于状态的不确定性关系。其中之一，假设一些自然对称性，导致Clauser-Horne-Shimony-Holt（CHSH）不等式的Tsirelson界。最后，我们表明，对于一个单一的系统的一个变种的信息因果关系称为信息内容的原则，在上述对称性，可以解释为上述意义上的不确定性关系。
The so-called preparation uncertainty that occurs in the quantum world can be understood well in purely operational terms, and its existence in any given theory, perhaps differently than in quantum mechanics, can be verified by examining only measurement statistics. Namely, one says that uncertainty occurs in some theory when for some pair of observables, there is no preparation that would exhibit deterministic statistics for both of them. However, the right-hand side of the uncertainty relation is not operational anymore if we do not insist that it is just the minimum of the left-hand side for a given theory. For example, in quantum mechanics, it is some function of two observables that must be computed within the quantum formalism. Also, while joint nonmeasurability of observables is an operational notion, the complementarity in Bohr's sense (i.e., in terms of information needed to describe the system) has not yet been expressed in purely operational terms. Here we propose a general operational framework that provides answers to the above issues. We introduce an operational definition of complementarity and further postulate that complementary observables have to exhibit uncertainty, which means that we propose to put the (operational) complementarity as the right-hand side of the uncertainty relation. In particular, we identify two different notions of uncertainty and complementarity for which the above principle holds in the quantum-mechanical realm. We also introduce postulates for the general measures of uncertainty and complementarity. In order to define quantifiers of complementarity we first turn to the simpler notion of independence that is defined solely in terms of the statistics of two observables. Importantly, for clean and extremal observables---i.e., ones that cannot be simulated irreducibly by other observables---any measure of independence reduces to the proper complementary measure. Finally, as an application of our general framework we define a number of complementarity indicators and show that they can be used to state uncertainty relations. One of them, assuming some natural symmetries, leads to the Tsirelson bound for the Clauser-Horne-Shimony-Holt (CHSH) inequality. Lastly, we show that for a single system a variant of information causality called the information content principle, under the above symmetries, can be interpreted as an uncertainty relation in the above sense.
影响因子：
2.9
作者：
Oszmaniec, Michal;Maciejewski, Filip B.;Puchala, Zbigniew
通讯作者：
Puchala, Zbigniew