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arXiv 1206.2897quant-ph
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共轭、滤子与量子力学

Conjugates, Filters and Quantum Mechanics

Alexander Wilce

备注：
33 pp. Minor corrections throughout; some revision of Appendix A
发表信息：
Quantum 3, 158 (2019)
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摘要：

有限维量子理论的约当结构是从抽象概率模型（每个模型由一组基本测量和一组凸态定义）的几个简单假设中以一种非常简单的方式推导出来的。关键的假设是，每个系统A可以通过非信令二分状态$η_A$与同构$\textit{conjugate}$系统$\overline{A}$配对，该二分状态$η_A$将A上的每个基本测量与其在$\overline{A}$上的对应物完美且一致地相关。在与复希尔伯特空间$\mathcal H$相关联的量子力学系统的情况下，共轭系统是与共轭希尔伯特空间$\overline{\mathcal H}$相关联的系统，并且$η_A$对应于${\mathcal H} \otimes \overline{\mathcal H}$上的标准最大纠缠EPR态。第二个要素是$\textit{reversible filter}$的概念，即独立地衰减与测量相关联的检测器的灵敏度的概率可逆过程。除了提供比大多数现有的有限维量子理论重建更大的灵活性之外，这里采用的方法还有一个优点，即不依赖于任何形式的“无限制”假设。也就是说，没有假设任意效应是物理可测量的，也没有假设任意族的物理可测量效应加起来等于单位效应，代表物理可及的可观测量。附录显示了如何一个版本的哈代的“子空间公理”可以取代几个假设本机本文，虽然在成本不允许超选择规则。

英文摘要：

The Jordan structure of finite-dimensional quantum theory is derived, in a conspicuously easy way, from a few simple postulates concerning abstract probabilistic models (each defined by a set of basic measurements and a convex set of states). The key assumption is that each system A can be paired with an isomorphic $\textit{conjugate}$ system, $\overline{A}$, by means of a non-signaling bipartite state $η_A$ perfectly and uniformly correlating each basic measurement on A with its counterpart on $\overline{A}$. In the case of a quantum-mechanical system associated with a complex Hilbert space $\mathcal H$, the conjugate system is that associated with the conjugate Hilbert space $\overline{\mathcal H}$, and $η_A$ corresponds to the standard maximally entangled EPR state on ${\mathcal H} \otimes \overline{\mathcal H}$. A second ingredient is the notion of a $\textit{reversible filter}$, that is, a probabilistically reversible process that independently attenuates the sensitivity of detectors associated with a measurement. In addition to offering more flexibility than most existing reconstructions of finite-dimensional quantum theory, the approach taken here has the advantage of not relying on any form of the "no restriction" hypothesis. That is, it is not assumed that arbitrary effects are physically measurable, nor that arbitrary families of physically measurable effects summing to the unit effect, represent physically accessible observables. An appendix shows how a version of Hardy's "subspace axiom" can replace several assumptions native to this paper, although at the cost of disallowing superselection rules.

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。

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