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arXiv · 1905.06729

The Modular Symmetry of Markov Maps

Jon Bannon·Jan Cameron·Kunal Mukherjee
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Abstract

A state-preserving automorphism of a von Neumann algebra induces a canonical unitary operator on the GNS Hilbert space of the state which fixes the vacuum. This unitary commutes with both the modular operator of the state and its modular conjugation. We prove an extension of this result for state-preserving unital completely positive maps.

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Jon Bannon, Jan Cameron, Kunal Mukherjee. 2019-05-16. The Modular Symmetry of Markov Maps. https://arxiv.org/abs/1905.06729

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