中科院数学与系统科学研究院
数学研究所
学术报告会
报告人：Prof. Runyao Duan (University of Technology, Sydney, Australia)
题 目：On zero-error communication via quantum channels in the presence of noiseless feedback
时 间：05.26（星期二）, 10:00--11:00
地 点：数学院南楼N913室
摘 要：We initiate the study of zero-error communication via quantum channels assisted by noiseless feedback link of unlimited quantum capacity, generalizing Shannon's zero-error communication theory with instantaneous feedback.
This capacity depends only on the linear span of Kraus operators of the channel, which generalizes the bipartite equivocation graph of a classical channel, and which we dub "non-commutative bipartite graph". We go on to show that the feedback-assisted capacity is non-zero (allowing for a constant amount of activating noiseless communication) if and only if the non-commutative bipartite graph is non-trivial, and give a number of equivalent characterizations. This result involves a far-reaching extension of the "conclusive exclusion" of quantum states [Pusey/Barrett/Rudolph, Nat Phys 8:475, 2012]. We then present an upper bound on the feedback-assisted zero-error capacity, motivated by a conjecture originally made by Shannon and proved by Ahlswede.
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