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Quantum reverse hypercontractivity

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If you have a question about this talk, please contact Mr. Cambyse Rouzé.

The theory of hypercontractivity and the closely related concept of log-Sobolev inequalities have become a fundamental tool in probability, computer science, and information theory. Recently, generalisations of these ideas to quantum information theory have also proven fruitful. In this talk I will discuss a quantum generalisation of a “reverse” version of a hypercontractive inequality, whose classical case was due to Mossel, Oleszkiewicz and Sen. Applications include a rapid mixing result for depolarising noise applied to large subspaces, and bounds on a quantum generalisation of non-interactive correlation distillation.

Joint work with Toby Cubitt, Michael Kastoryano and Kristan Temme. arXiv:1504.06143.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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