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Published October 2015 | Published + Submitted
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Quantum reverse hypercontractivity

Cubitt, Toby
Kastoryano, Michael
Montanaro, Ashley
Temme, Kristan
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Abstract

We develop reverse versions of hypercontractive inequalities for quantum channels. By generalizing classical techniques, we prove a reverse hypercontractive inequality for tensor products of qubit depolarizing channels. We apply this to obtain a rapid mixing result for depolarizing noise applied to large subspaces and to prove bounds on a quantum generalization of non-interactive correlation distillation.

Additional Information

© 2015 AIP Publishing LLC. Received 13 June 2015; accepted 1 October 2015; published online 19 October 2015. This work was initiated at the BIRS workshop 15w5098, "Hypercontractivity and Log Sobolev Inequalities in Quantum Information Theory." We would like to thank BIRS and the Banff Centre for their hospitality. We would also like to thank Mark Wilde for pointing out Ref. 24 and an anonymous referee for helpful comments. M.K. was supported by the Carlsbergfond and the Villum foundation. A.M. was supported by the UK EPSRC under Early Career Fellowship EP/L021005/1. K.T. was supported by the Institute for Quantum Information and Matter, a NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation (Grants Nos. PHY-0803371 and PHY-1125565). T.S.C. is supported by the Royal Society.

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