Versatile relative entropy bounds for quantum networks

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Title: Versatile relative entropy bounds for quantum networks
Author(s): Rigovacca, L
Kato, G
Bauml, S
Kim, MS
Munro, WJ
Azuma, K
Item Type: Journal Article
Abstract: We provide a versatile upper bound on the number of maximally entangled qubits, or private bits, shared by two parties via a generic adaptive communication protocol over a quantum network when the use of classical communication is not restricted. Although our result follows the idea of Azuma et al (2016 Nat. Commun. 7 13523) of splitting the network into two parts, our approach relaxes their strong restriction, consisting of the use of a single entanglement measure in the quantification of the maximum amount of entanglement generated by the channels. In particular, in our bound the measure can be chosen on a channel-by-channel basis, in order to make it as tight as possible. This enables us to apply the relative entropy of entanglement, which often gives a state-of-the-art upper bound, on every Choi-simulable channel in the network, even when the other channels do not satisfy this property. We also develop tools to compute, or bound, the max-relative entropy of entanglement for channels that are invariant under phase rotations. In particular, we present an analytical formula for the max-relative entropy of entanglement of the qubit amplitude damping channel.
Publication Date: 24-Jan-2018
Date of Acceptance: 7-Dec-2017
URI: http://hdl.handle.net/10044/1/57145
DOI: https://dx.doi.org/10.1088/1367-2630/aa9fcf
ISSN: 1367-2630
Publisher: Institute of Physics (IoP) and Deutsche Physikalische Gesellschaft
Journal / Book Title: New Journal of Physics
Volume: 20
Copyright Statement: © 2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische. 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 (https://creativecommons.org/licenses/by/3.0/)
Sponsor/Funder: Commission of the European Communities
Engineering & Physical Science Research Council (E
The Royal Society
Samsung Electronics Co Ltd
Funder's Grant Number: 317232
EP/K034480/1
WM140063
N/A
Keywords: Science & Technology
Physical Sciences
Physics, Multidisciplinary
Physics
quantum communication
quantum networks
quantum information
KEY DISTRIBUTION
SQUASHED ENTANGLEMENT
BROADCAST CHANNELS
LINEAR OPTICS
BELL THEOREM
STATES
COMPUTATION
PRIVATE
COMMUNICATION
CRYPTOGRAPHY
quant-ph
quant-ph
Science & Technology
Physical Sciences
Physics, Multidisciplinary
Physics
quantum communication
quantum networks
quantum information
KEY DISTRIBUTION
SQUASHED ENTANGLEMENT
BROADCAST CHANNELS
LINEAR OPTICS
BELL THEOREM
STATES
COMPUTATION
PRIVATE
COMMUNICATION
CRYPTOGRAPHY
02 Physical Sciences
Fluids & Plasmas
Publication Status: Published
Article Number: ARTN 013033
Appears in Collections:Quantum Optics and Laser Science
Physics
Faculty of Natural Sciences



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