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Zero-Error Classical Channel Capacity and Simulation Cost Assisted by Quantum Non-Signalling Correlations

Thursday 3rd October 2013 - 14:00 to 15:00
INI Seminar Room 1
We study the one-shot zero-error classical capacity of quantum channels assisted by quantum non-signalling correlations, and the reverse problem of exact simulation. Both lead to simple semi-definite programmings whose solutions can be given in terms of the conditional min-entropies. We show that the asymptotic simulation cost is precisely the conditional min-entropy of the Choi-Jamiolkowski matrix of the given channel. For classical-quantum channels, the asymptotic capacity is reduced to a quantum fractional packing number suggested by Harrow, which leads to an operational interpretation of the celebrated Lovasz function as the zero-error classical capacity of a graph assisted by quantum non-signalling correlations. This talk is based on a joint work with Andreas Winter (UAB).
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons