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arXiv · 2004.14751

Two constructive proofs on d-majorization and thermo-majorization

Naoto Shiraishi
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Abstract

Two constructive proofs on d-majorization and thermo-majorization are provided. In the first part, we present a diagrammatic proof of the equivalence between d-majorization and the existence of a proper stochastic matrix. We explicitly construct the desired stochastic matrix by using a graphical argument. In the second part, we present a constructive proof of the equivalence between the Gibbs-preserving map and thermal operation in classical systems. We construct the desired thermal operation and a heat bath which emulates any Gibbs-preserving map with an arbitrary accuracy.

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Naoto Shiraishi. 2020-04-30. Two constructive proofs on d-majorization and thermo-majorization. https://doi.org/10.1088/1751-8121%2Fabb041

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