量子相空间中的弱值与模变元
Weak Values and Modular Variables From a Quantum Phase Space Perspective
摘要：
我们通过\textit{quantum phase space}方法解决Aharonov及其合作者引入的两个主要概念发展：\textit{modular variables}的概念被设计来解释量子动力学非定域性的现象，以及用于量子力学的\textit{two-state formalism}，其是导致\textit{weak values.}发现的量子物理学的追溯时间对称解释。我们提出量子相空间结构以统一的方式作为这些深刻的物理见解的基础。为此，我们简要地回顾了Weyl-Wigner和相干态形式以及量子射影空间的固有辛结构，以便更深入地理解弱值概念。我们还回顾了Schwinger的有限量子运动学，使我们可以应用这种离散形式主义来理解Aharonov的模块化变量的概念，在文献中已经提出了不同的方式。我们讨论了为什么我们相信这确实是模块变量概念的正确运动学框架，以及这如何可能照亮量子动力学非定域性和运动学非定域性之间的物理区别，通常与纠缠量子系统相关。
英文摘要：
We address two major conceptual developments introduced by Aharonov and collaborators through a \textit{quantum phase space} approach: the concept of \textit{modular variables} devised to explain the phenomena of quantum dynamical non-locality and the \textit{two-state formalism} for Quantum Mechanics which is a retrocausal time-symmetric interpretation of quantum physics which led to the discovery of \textit{weak values.} We propose that a quantum phase space structure underlies these profound physical insights in a unifying manner. For this, we briefly review the Weyl-Wigner and the coherent state formalisms as well as the inherent symplectic structures of quantum projective spaces in order to gain a deeper understanding of the weak value concept. We also review Schwinger's finite quantum kinematics so that we may apply this discrete formalism to understand Aharonov's modular variable concept in a different manner that has been proposed before in the literature. We discuss why we believe that this\ is indeed the correct kinematic framework for the modular variable concept and how this may shine some light on the physical distinction between quantum dynamical non-locality and the kinematic non-locality, generally associated with entangled quantum systems.
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