逐步推导量子力学的代数结构（或通过连接不相容的可观测量从非扰动到量子关联）
Step-by-step derivation of the algebraic structure of quantum mechanics (or from nondisturbing to quantum correlations by connecting incompatible observables)
摘要：
近年来，从简单公理出发导出量子形式和量子关联集合引起了人们极大的兴趣。在本文中，我们提供了一个逐步推导的量子形式主义，解决这两个问题，并帮助我们理解为什么这种形式主义是因为它是。我们从一个只包含实值观测量、态和一个（未指定的）状态更新的无结构系统开始，逐步确定使量子力学的代数结构被它同化的理论无关条件。在论文的第一部分，我们基本上导出了量子形式主义的所有“交换部分”，即，所有定义和定理，不涉及代数运算之间的不兼容的可观，如投影，斯派克的原则，和频谱定理;在统计水平上，系统是无干扰的，并满足排他性原则在这个阶段。在论文的第二部分，我们通过考虑纯态之间的跃迁概率来连接不相容的观测量。这种联系是将我们的系统嵌入希尔伯特空间并从无扰到量子关联所需的最后一步。
英文摘要：
Recently there has been much interest in deriving the quantum formalism and the set of quantum correlations from simple axioms. In this paper, we provide a step-by-step derivation of the quantum formalism that tackles both these problems and helps us to understand why this formalism is as it is. We begin with a structureless system that only includes real-valued observables, states and a (not specified) state update, and we gradually identify theory-independent conditions that make the algebraic structure of quantum mechanics be assimilated by it. In the first part of the paper, we derive essentially all the "commutative part" of the quantum formalism, i.e., all definitions and theorems that do not involve algebraic operations between incompatible observables, such as projections, Specker's principle, and the spectral theorem; at the statistical level, the system is nondisturbing and satisfies the exclusivity principle at this stage. In the second part of the paper, we connect incompatible observables by taking transition probabilities between pure states into account. This connection is the final step needed to embed our system in a Hilbert space and to go from nondisturbing to quantum correlations.
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。
