Thermodynamics and the structure of quantum theory
Thermodynamics and the structure of quantum theory
复制标题
DOI：
10.1088/1367-2630/aa68ef
复制
发表时间：
2016-08
影响因子：
3.3
通讯作者：
Marius Krumm;H. Barnum;J. Barrett;Markus P. Müller
中科院分区：
文献类型：
--
作者：
Marius Krumm;H. Barnum;J. Barrett;Markus P. Müller
尽管量子理论的形式主义在经验上取得了巨大的成功，但它仍然提出了一些基本问题：为什么自然界是用复杂的希尔伯特空间来描述的，我们可以合理地期望在某些物理学领域中找到什么样的修改？在这里，我们通过研究与热力学的相容性如何约束量子理论的结构来解决这些问题。我们采用两个假设，任何概率理论与合理的热力学行为应该可以说满足。在广义概率理论的框架内，我们表明，这些假设已经暗示了量子理论的重要方面，如自对偶性和类似物的投影测量，子空间和特征值。然而，他们仍然可能承认量子力学之外的一类理论。使用冯诺依曼的思想实验，我们表明，这些理论承认一个一致的热力学概念熵，并证明第二定律持有投影测量和混合程序。此外，我们研究了额外的熵类量的测量概率和凸分解概率的基础上，并揭示了这些数量和Sorkin的高阶干扰的概念之间的关系。
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some regimes of physics? Here we address these questions by studying how compatibility with thermodynamics constrains the structure of quantum theory. We employ two postulates that any probabilistic theory with reasonable thermodynamic behaviour should arguably satisfy. In the framework of generalised probabilistic theories, we show that these postulates already imply important aspects of quantum theory, like self-duality and analogues of projective measurements, subspaces and eigenvalues. However, they may still admit a class of theories beyond quantum mechanics. Using a thought experiment by von Neumann, we show that these theories admit a consistent thermodynamic notion of entropy, and prove that the second law holds for projective measurements and mixing procedures. Furthermore, we study additional entropy-like quantities based on measurement probabilities and convex decomposition probabilities, and uncover a relation between one of these quantities and Sorkin’s notion of higher-order interference.