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arXiv 1608.04461quant-phhep-thmath-phmath.MP
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热力学与量子理论的结构

Thermodynamics and the structure of quantum theory

Marius Krumm, Howard Barnum, Jonathan Barrett, Markus P. Mueller

摘要:

尽管量子理论在经验上取得了巨大的成功,但它的形式主义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它的哪些修改?在这里,我们解决这些问题,通过研究如何与热力学相容约束结构的量子理论。我们采用了两个假设,任何具有合理热力学行为的概率理论都应该满足这两个假设。在广义概率理论的框架下,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,他们可能仍然承认一类超越量子力学的理论。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熵热力学概念,并证明第二定律适用于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。

英文摘要:

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 behavior should arguably satisfy. In the framework of generalized 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.

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