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Quantum Channel Simulation and the Channel's Smooth Max-Information

Presented by: 
Kun Fang University of Technology Sydney
Tuesday 24th July 2018 - 11:45 to 12:30
INI Seminar Room 1
Co-authors: Xin Wang (Centre for Quantum Software and Information, University of Technology Sydney), Marco Tomamichel (Centre for Quantum Software and Information, University of Technology Sydney), Mario Berta (Department of Computing, Imperial College London)

We study the general framework of quantum channel simulation, that is, the ability of a quantum channel to simulate another one using different classes of codes. First, we show that the minimum error of simulation and the one-shot quantum simulation cost under no-signalling assisted codes are efficiently computable via semidefinite programming. Second, we introduce the channel's smooth max-information, which can be seen as a one-shot generalization of the mutual information of a quantum channel. We provide an exact operational interpretation of the channel's smooth max-information as the one-shot quantum simulation cost. Third, we derive the asymptotic equipartition property (AEP) of the channel's smooth max-information, i.e., it converges to the quantum mutual information of the channel in the independent and identically distributed asymptotic limit. This implies the quantum reverse Shannon theorem (QRST) in the presence of no-signalling correlations. Finally, we explore finite blocklength simulation cost of fundamental quantum channels and provide both numerical and analytical solutions.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons