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Amortization does not enhance the max-Rains information of a quantum channel

Berta, Mario and Wilde, Mark M. (2018) Amortization does not enhance the max-Rains information of a quantum channel. New Journal of Physics, 20 (5). Art. No. 053044. ISSN 1367-2630. https://resolver.caltech.edu/CaltechAUTHORS:20180518-131642361

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Abstract

Given an entanglement measure E, the entanglement of a quantum channel is defined as the largest amount of entanglement E that can be generated from the channel, if the sender and receiver are not allowed to share a quantum state before using the channel. The amortized entanglement of a quantum channel is defined as the largest net amount of entanglement E that can be generated from the channel, if the sender and receiver are allowed to share an arbitrary state before using the channel. Our main technical result is that amortization does not enhance the entanglement of an arbitrary quantum channel, when entanglement is quantified by the max-Rains relative entropy. We prove this statement by employing semi-definite programming (SDP) duality and SDP formulations for the max-Rains relative entropy and a channel's max-Rains information, found recently in Wang et al (arXiv:1709.00200). The main application of our result is a single-letter, strong converse, and efficiently computable upper bound on the capacity of a quantum channel for transmitting qubits when assisted by positive-partial-transpose preserving (PPT-P) channels between every use of the channel. As the class of local operations and classical communication (LOCC) is contained in PPT-P, our result establishes a benchmark for the LOCC-assisted quantum capacity of an arbitrary quantum channel, which is relevant in the context of distributed quantum computation and quantum key distribution.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1088/1367-2630/aac153DOIArticle
https://arxiv.org/abs/1709.04907arXivDiscussion Paper
ORCID:
AuthorORCID
Berta, Mario0000-0002-0428-3429
Wilde, Mark M.0000-0002-3916-4462
Additional Information:©2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. RECEIVED. 20 January 2018. REVISED 20 April 2018. ACCEPTED FOR PUBLICATION 30 April 2018. PUBLISHED 18 May 2018. We are grateful to Omar Fawzi, Xin Wang, David Reeb, Siddhartha Das, and Andreas Winter for discussions related to the topic of this paper. We also thank the anonymous referee for comments that helped improve our paper, in particular for comments about the usefulness of PPT-P channels. Part of this work was done during the workshop 'Beyond IID. in Information Theory,' hosted by the Institute for Mathematical Sciences, Singapore, 24–28 July 2017. MB acknowledges funding by the SNSF through a fellowship. MMW acknowledges support from the Office of Naval Research and the National Science Foundation under grant no. 1350397.
Group:Institute for Quantum Information and Matter, IQIM
Funders:
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)UNSPECIFIED
Office of Naval Research (ONR)UNSPECIFIED
NSFCCF-1350397
Subject Keywords:max-Rains information, LOCC-assisted quantum capacity, semi-definite programming
Issue or Number:5
Record Number:CaltechAUTHORS:20180518-131642361
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180518-131642361
Official Citation:Mario Berta and Mark M Wilde 2018 New J. Phys. 20 053044
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86454
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:18 May 2018 20:53
Last Modified:03 Oct 2019 19:43

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