Von Neumann's information engine without the spectral theorem
Von Neumann's information engine without the spectral theorem
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没有谱定理的冯诺依曼信息引擎
DOI：
10.1103/physrevresearch.4.033091
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发表时间：
2022
影响因子：
4.2
通讯作者：
Buscemi Francesco
中科院分区：
文献类型：
--
作者：
Minagawa Shintaro;Arai Hayato;Buscemi Francesco
冯·诺依曼通过假设热力学第二定律在一个涉及半透膜和量子标记粒子的理想气体的思想实验中的有效性，获得了量子态熵的公式。尽管冯·诺依曼的论证在很大程度上是可操作的，但在使用谱定理时，他的论证偏离了可操作的叙述。在这项工作中，我们表明，冯诺依曼的论点中的光谱定理的作用，可以接管的可重复性和可逆性的操作假设，并使用这些，我们能够探索的第二定律的后果，也在理论，不具备一个独特的光谱分解。作为一个副产品，我们获得的Groenewold-Ozawa信息增益作为一个自然的单调为一个合适的顺序的仪器，它提供了一个有效的量子理论和超越的操作解释。
Von Neumann obtained the formula for the entropy of a quantum state by assuming the validity of the second law of thermodynamics in a thought experiment involving semipermeable membranes and an ideal gas of quantum-labeled particles. Despite being operational for the most part, von Neumann's argument departs from an operational narrative in its use of the spectral theorem. In this work, we show that the role of the spectral theorem in von Neumann's argument can be taken over by the operational assumptions of repeatability and reversibility, and, using these, we are able to explore the consequences of the second law also in theories that do not possess a unique spectral decomposition. As a byproduct, we obtain the Groenewold-Ozawa information gain as a natural monotone for a suitable ordering of instruments, providing it with an operational interpretation valid in quantum theory and beyond.