A semidefinite programming upper bound of quantum capacity

Abstract

© 2016 IEEE.Recently the power of positive partial transpose preserving (PPTp) and no-signalling (NS) codes in quantum communication has been studied. We continue with this line of research and show that the NS/PPTp/NS∩PPTp codes assisted zero-error quantum capacity depends only on the non-commutative bipartite graph of the channel and the one-shot case can be computed efficiently by semidefinite programming (SDP). As an example, the activated PPTp codes assisted zero-error quantum capacity is carefully studied. We then present a general SDP upper bound of quantum capacity and show it is always smaller than or equal to the ‘Partial transposition bound’ introduced by Holevo and Werner, and the inequality could be strict. This upper bound is found to be additive, and thus is an upper bound of the potential PPTp assisted quantum capacity as well. We further demonstrate that our bound is strictly better than several previously known upper bounds for an explicit class of quantum channels. .

Publication
2016 IEEE International Symposium on Information Theory (ISIT)
Xin Wang
Xin Wang
Associate Professor

The main focus of my research is to better understand the limits of information processing with quantum systems and the power of quantum artificial intelligence.