论文标题
von Neumann的信息引擎没有光谱定理
Von Neumann's information engine without the spectral theorem
论文作者
论文摘要
冯·诺伊曼（Von Neumann）通过在涉及半透明膜和量子标记颗粒的理想气体的思想实验中假设热力学的第二定律的有效性，从而获得了量子态熵的公式。尽管在大多数情况下运作，但冯·诺伊曼（Von Neumann）的论点在使用光谱定理方面与操作叙述至关重要。在这项工作中，我们表明，光谱定理在冯·诺伊曼（Von Neumann）的论点中的作用可以通过可重复性和可逆性的操作假设来接管，并且使用这些假设我们能够探索第二定律的后果，这些理论也不具有独特的光谱分解。作为副产品，我们获得了groenewold-ozawa信息作为适当订购工具的自然单调，从而为其提供了在量子理论及其他方面有效的操作解释。
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 in the most part, von Neumann's argument crucially 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.
