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Title: Quantum reverse hypercontractivity

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.

Authors:
 [1];  [2];  [3];  [4]
  1. Department of Computer Science, University College London, London, United Kingdom and Centre for Quantum Information and Foundations, DAMTP, University of Cambridge, Cambridge (United Kingdom)
  2. NBIA, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen (Denmark)
  3. School of Mathematics, University of Bristol, Bristol (United Kingdom)
  4. Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125 (United States)
Publication Date:
OSTI Identifier:
22479541
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 10; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATIONS; NOISE; QUANTUM MECHANICS; TENSORS

Citation Formats

Cubitt, Toby, Kastoryano, Michael, Montanaro, Ashley, and Temme, Kristan. Quantum reverse hypercontractivity. United States: N. p., 2015. Web. doi:10.1063/1.4933219.
Cubitt, Toby, Kastoryano, Michael, Montanaro, Ashley, & Temme, Kristan. Quantum reverse hypercontractivity. United States. doi:10.1063/1.4933219.
Cubitt, Toby, Kastoryano, Michael, Montanaro, Ashley, and Temme, Kristan. 2015. "Quantum reverse hypercontractivity". United States. doi:10.1063/1.4933219.
@article{osti_22479541,
title = {Quantum reverse hypercontractivity},
author = {Cubitt, Toby and Kastoryano, Michael and Montanaro, Ashley and Temme, Kristan},
abstractNote = {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.},
doi = {10.1063/1.4933219},
journal = {Journal of Mathematical Physics},
number = 10,
volume = 56,
place = {United States},
year = 2015,
month =
}
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