A semidefinite programming upper bound of quantum capacity

Xin Wang, Runyao Duan
July 2016
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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. .

Type
Conference paper
Publication
2016 IEEE International Symposium on Information Theory (ISIT)
Bipartite graph Channel capacity Holevo PPTp codes Programming Quantum computing Quantum mechanics SDP Upper bound Werner assisted zero error quantum capacity graph theory mathematical programming noncommutative bipartite graph nosignalling codes partial transposition bound positive partial transpose preserving quantum capacity superactivation quantum channels quantum communication semidefinite programming telecommunication channels telecommunication signalling
Xin Wang
Xin Wang
Associate Professor

Prof. Xin Wang founded the QuAIR Lab at HKUST (Guangzhou) in June 2023. His research aims to advance our understanding of the limits of information processing with quantum systems and the potential of quantum artificial intelligence. His current interests include quantum algorithms, quantum resource theory, quantum machine learning, quantum computer architecture, and quantum error processing. Prior to establishing the QuAIR Lab, Prof. Wang was a Staff Researcher at the Institute for Quantum Computing at Baidu Research, where he focused on quantum computing research and the development of the Baidu Quantum Platform. Notably, he led the development of Paddle Quantum, a Python library for quantum machine learning. From 2018 to 2019, he was a Hartree Postdoctoral Fellow at the Joint Center for Quantum Information and Computer Science (QuICS) at the University of Maryland, College Park. Prof. Wang received his Ph.D. in quantum information from the University of Technology Sydney in 2018, under the supervision of Prof. Runyao Duan and Prof. Andreas Winter. He obtained his B.S. in mathematics (Wu Yuzhang Honors) from Sichuan University in 2014.