Cubitt, Toby and Kastoryano, Michael and Montanaro, Ashley and Temme, Kristan (2015) Quantum reverse hypercontractivity. Journal of Mathematical Physics, 56 (10). Art. No. 102204. ISSN 0022-2488. doi:10.1063/1.4933219. https://resolver.caltech.edu/CaltechAUTHORS:20151201-094310055
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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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| 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. | ||||||||||||||||||||
| Group: | Institute for Quantum Information and Matter | ||||||||||||||||||||
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| Issue or Number: | 10 | ||||||||||||||||||||
| DOI: | 10.1063/1.4933219 | ||||||||||||||||||||
| Record Number: | CaltechAUTHORS:20151201-094310055 | ||||||||||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20151201-094310055 | ||||||||||||||||||||
| Official Citation: | Quantum reverse hypercontractivity Cubitt, Toby and Kastoryano, Michael and Montanaro, Ashley and Temme, Kristan, Journal of Mathematical Physics, 56, 102204 (2015), DOI:http://dx.doi.org/10.1063/1.4933219 | ||||||||||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||||||||
| ID Code: | 62489 | ||||||||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||||||||
| Deposited By: | Tony Diaz | ||||||||||||||||||||
| Deposited On: | 03 Dec 2015 03:24 | ||||||||||||||||||||
| Last Modified: | 10 Nov 2021 23:03 |
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