Related papers: Von Neumann's information engine without the spectral theorem

Von Neumann's information engine without the spectral theorem

URL: http://arxiv.org/abs/2203.05258v2
Date: Tue, 2 Aug 2022 12:05:58 GMT
Title: Von Neumann's information engine without the spectral theorem
Authors: Shintaro Minagawa, Hayato Arai, Francesco Buscemi
Abstract summary: 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. As a byproduct, we obtain the Groenewold--Ozawa information gain as a natural monotone for a suitable ordering of instruments.
Score: 1.933681537640272
License: http://creativecommons.org/licenses/by/4.0/
Abstract: 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.

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