arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1807.01583quant-ph
收藏

从关系性质看量子力学，第III部分：路径积分实现

Quantum Mechanics from Relational Properties, Part III: Path Integral Implementation

Jianhao M. Yang

备注：
16 pages, 2 figures. Closely matches the published version. Introduction section may have overlap with arXiv:1803.04843, arXiv:1706.01317 as they are parts of a same series
发表信息：
Sci. Rep. 11, 8613 (2021)
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

量子力学的关系表述是基于这样一种思想，即量子系统之间的关系性质，而不是量子系统的独立性质，是构造量子力学的最基本要素。在最近的一篇论文中（J. M. Yang，Sci. Rep. 8：13305，2018），基本的关系量子力学框架被制定为导出量子概率，玻恩规则，薛定谔方程和测量理论。本文从三个方面进一步扩展了重新表述的努力。首先，它对计算测量概率的框架背后的关键概念给出了更清晰的解释。其次，我们通过扩展路径积分公式，给出了关系概率幅的具体实现。该实现不仅阐明了关联几率幅的物理意义，而且使我们能够优雅地解释双缝实验，描述被测系统与一系列测量系统之间的相互作用历史，以及基于路径积分和影响泛函计算纠缠熵.作为回报，该实现通过完成对测量概率可以被计算为概率幅度的模平方的解释，为路径积分本身带来了新的见解。最后，我们阐明了我们的重新表述和量子参考系理论之间的联系。完整的量子力学关系式需要结合现有的工作和量子参考系理论。

英文摘要：

Relational formulation of quantum mechanics is based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum mechanics. In a recent paper (J. M. Yang, Sci. Rep. 8:13305, 2018), basic relational quantum mechanics framework is formulated to derive quantum probability, Born's Rule, Schrödinger Equations, and measurement theory. This paper further extends the reformulation effort in three aspects. First, it gives a clearer explanation of the key concepts behind the framework to calculate measurement probability. Second, we provide a concrete implementation of the relational probability amplitude by extending the path integral formulation. The implementation not only clarifies the physical meaning of the relational probability amplitude, but also allows us to elegantly explain the double slit experiment, to describe the interaction history between the measured system and a series of measuring systems, and to calculate entanglement entropy based on path integral and influence functional. In return, the implementation brings back new insight to path integral itself by completing the explanation on why measurement probability can be calculated as modulus square of probability amplitude. Lastly, we clarify the connection between our reformulation and the quantum reference frame theory. A complete relational formulation of quantum mechanics needs to combine the present works with the quantum reference frame theory.

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。

↑