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A semidefinite programming upper bound of quantum capacity | IEEE Conference Publication | IEEE Xplore

A semidefinite programming upper bound of quantum capacity


Abstract:

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 r...Show More

Abstract:

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 QΓ 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 QΓ is strictly better than several previously known upper bounds for an explicit class of quantum channels. Finally, we show that QΓ can be used to bound the super-activation of quantum capacity.
Date of Conference: 10-15 July 2016
Date Added to IEEE Xplore: 11 August 2016
ISBN Information:
Electronic ISSN: 2157-8117
Conference Location: Barcelona, Spain

References

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