Bounds on the Distance Between a Unital Quantum Channel and the Convex Hull of Unitary Channels

Nengkun Yu; Runyao Duan; Quanhua Xu

doi:10.1109/TIT.2016.2641447

Bounds on the Distance Between a Unital Quantum Channel and the Convex Hull of Unitary Channels

Nengkun Yu
, Runyao Duan
, Quanhua Xu

Computer Science

University of Technology Sydney
CAS - Academy of Mathematics and System Sciences
Harbin Institute of Technology
CNRS
Institut universitaire de France

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Motivated by the recent resolution of asymptotic quantum birkhoff conjecture (AQBC), we attempt to estimate the distance between a given unital quantum channel and the convex hull of unitary channels. We provide two lower bounds on this distance by employing techniques from quantum information and operator algebras, respectively. We then show how to apply these results to construct some explicit counterexamples to AQBC. We also point out an interesting connection between the Grothendieck's inequality and AQBC.

Original language	English
Article number	7790874
Pages (from-to)	1299-1310
Number of pages	12
Journal	IEEE Transactions on Information Theory
Volume	63
Issue number	2
DOIs	https://doi.org/10.1109/TIT.2016.2641447
State	Published - Feb 2017

Keywords

Asymptotic quantum birkhoff conjecture
diamond norm
Grothendieck inequality
Schur multiplier

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10.1109/TIT.2016.2641447

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abstract = "Motivated by the recent resolution of asymptotic quantum birkhoff conjecture (AQBC), we attempt to estimate the distance between a given unital quantum channel and the convex hull of unitary channels. We provide two lower bounds on this distance by employing techniques from quantum information and operator algebras, respectively. We then show how to apply these results to construct some explicit counterexamples to AQBC. We also point out an interesting connection between the Grothendieck's inequality and AQBC.",

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KW - Asymptotic quantum birkhoff conjecture

KW - diamond norm

KW - Grothendieck inequality

KW - Schur multiplier

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Bounds on the Distance Between a Unital Quantum Channel and the Convex Hull of Unitary Channels

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Keywords

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