Hofmann Holger F
Graduate School of Advanced Science and Engineering, Hiroshima University, Kagamiyama 1-3-1, Higashi Hiroshima 739-8530, Japan.
Entropy (Basel). 2024 Aug 26;26(9):725. doi: 10.3390/e26090725.
Quantum contextuality describes situations where the statistics observed in different measurement contexts cannot be explained by a measurement of the independent reality of the system. The most simple case is observed in a three-dimensional Hilbert space, with five different measurement contexts related to each other by shared measurement outcomes. The quantum formalism defines the relations between these contexts in terms of well-defined relations between operators, and these relations can be used to reconstruct an unknown quantum state from a finite set of measurement results. Here, I introduce a reconstruction method based on the relations between the five measurement contexts that can violate the bounds of non-contextual statistics. A complete description of an arbitrary quantum state requires only five of the eight elements of a Kirkwood-Dirac quasiprobability, but only an overcomplete set of eleven elements provides an unbiased description of all five contexts. A set of five fundamental relations between the eleven elements reveals a deterministic structure that links the five contexts. As illustrated by a number of examples, these relations provide a consistent description of contextual realities for the measurement outcomes of all five contexts.
在不同测量语境中观察到的统计数据无法通过对系统独立实在性的测量来解释。最简单的情况出现在三维希尔伯特空间中，其中五个不同的测量语境通过共享的测量结果相互关联。量子形式体系根据算符之间明确的关系定义了这些语境之间的关系，并且这些关系可用于从有限的一组测量结果中重构未知的量子态。在此，我引入一种基于五个测量语境之间关系的重构方法，该方法可能违反非语境统计的界限。对任意量子态的完整描述仅需要柯克伍德 - 狄拉克准概率的八个元素中的五个，但只有一组超完备的十一个元素才能对所有五个语境提供无偏描述。十一个元素之间的一组五个基本关系揭示了一种将五个语境联系起来的确定性结构。正如许多例子所示，这些关系为所有五个语境的测量结果的语境实在性提供了一致的描述。
