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

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Mathematical Challenges in Quantum Information

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).

This talk is part of the Isaac Newton Institute Seminar Series series.

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