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

Publisher:
Institute of Electrical and Electronics Engineers
Publication Type:
Journal Article
Citation:
IEEE Transactions on Information Theory, 2017, 63 (2), pp. 1299 - 1310
Issue Date:
2017-02-01
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© 2016 IEEE. 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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