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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.
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The possibility of such a proof was communicated to us by an anonymous referee of QIP’2012 in his/her review report and by Watrous in private conversation with the first named author (N. Yu). We would like to thank them for their helpful and generous comments
2012
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