No-Signalling Assisted Zero-Error Capacity of Quantum Channels and an Information Theoretic Interpretation of the Lovász Number Full version at: arXiv:1409.3426

We study the one-shot zero-error classical capacity of quantum channels assisted by quantum no-signalling correlations, and the reverse problem of simulation. Both lead to simple semi-definite programmings whose solutions can be given in terms of conditional min-entropies. We show that the asymptotic simulation cost is precisely the conditional min-entropy of the ChoiJamiołkowski 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 the first information-theoretic operational interpretation of the celebrated Lovász θ function as the zero-error classical capacity of a graph assisted by quantum no-signalling correlations.