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arXiv · 1909.01906

Relative entropy for von Neumann subalgebras

Li Gao·Marius Junge·Nicholas LaRacuente
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Abstract

We revisit the connection between index and relative entropy for an inclusion of finite von Neumann algebras. We observe that the Pimsner-Popa index connects to sandwiched Renyi $p$-relative entropy for all $1/2\le p\le \infty$, including Umegaki's relative entropy at $p=1$. Based on that, we introduce a new notation of relative entropy to a subalgebra which generalizes subfactors index. This relative entropy has application in estimating decoherence time of quantum Markov semigroups.

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Li Gao, Marius Junge, Nicholas LaRacuente. 2019-09-04. Relative entropy for von Neumann subalgebras. https://doi.org/10.1142/s0129167x20500469

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