Ke Li's lemma for quantum hypothesis testing in general von Neumann algebras

10/05/2020

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by   Yan Pautrat, et al.

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A lemma stated by Ke Li in <cit.> has been used in e.g.<cit.> for various tasks in quantum hypothesis testing, data compression with quantum side information or quantum key distribution. This lemma was proven in finite dimension only (with an easy extension to type I von Neumann algebras). Here we show that the use of modular theory allows to give more transparent meaning to the objects constructed by the lemma, and to prove it for general von Neumann algebras.