具有上下文标记观测量的量子力学
Quantum Mechanics with Contextually Labeled Observables
摘要：
在默认上下文理论中，表示测量结果的随机变量被上下文标记，即，不仅取决于他们测量什么，而且取决于测量是在什么条件下（在什么背景下）进行的，包括但不能简化为与给定测量“一起”进行的其他测量。在本文中，我们建议生成这些随机变量的量子可观测量也被标记为上下文，使得不同上下文中的可观测量的集合不相交。一个量子可观测量被定义为一个由可观测量的标签和希尔伯特空间中的自伴算子组成的对。如果系统始终连接（即，服从“非干扰”、“非侵入性”或“非信号”条件），在不同背景下测量相同属性的可观测量具有相同的算子。一组具有联合分布的随机变量由可交换观测量表示。然而，反过来就不正确了：来自不同背景的随机变量不具有联合分布，不管相应的可观测量是否可交换。我们说明了这一观点的观测量推导出Tsirelson界一贯连接循环系统的秩3。
英文摘要：
In the Contextuality-by-Default theory random variables representing measurement outcomes are labeled contextually, i.e., not only by what they measure but also under what conditions (in what contexts) the measurements are made, including but not reducible to what other measurements are made "together" with the given one. We propose in this paper that the quantum observables generating these random variables be labeled contextually as well, making the sets of the observables in different contexts disjoint. A quantum observable is defined as a pair consisting of the observable's label and a self-adjoint operator in a Hilbert space. If a system is consistently connected (i.e., obeys "non-disturbance," "non-invasivenes," or "non-signaling" conditions), the observables measuring the same property in different contexts have the same operator. A set of random variables possessing a joint distribution is represented by commuting observables. The reverse, however, is not true: random variables from different contexts do not have a joint distribution irrespective of whether the corresponding observables commute. We illustrate this view of observables by deriving the Tsirelson bound for consistently connected cyclic systems of rank 3.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
