Quantum reverse hypercontractivity

Toby Cubitt; Michael Kastoryano; Ashley Montanaro; Kristan Temme

doi:10.1063/1.4933219

Quantum reverse hypercontractivity

Toby Cubitt, Michael Kastoryano, Ashley Montanaro, Kristan Temme

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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.

Original language	English
Article number	102204
Number of pages	11
Journal	Journal of Mathematical Physics
Volume	56
Issue number	10
DOIs	https://doi.org/10.1063/1.4933219
Publication status	Published - 19 Oct 2015

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New insights in quantum algorithms and complexity
Montanaro, A. M. R. (Principal Investigator)
31/07/14 → 30/06/20
Project: Research
New insights in quantum algorithms and complexity
Montanaro, A. M. R. (Principal Investigator)
31/07/14 → 30/07/19
Project: Research

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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.",

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AU - Temme, Kristan

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AB - 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.

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M3 - Article (Academic Journal)

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Quantum reverse hypercontractivity

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New insights in quantum algorithms and complexity

New insights in quantum algorithms and complexity

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