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One-shot Marton inner bound for classical-quantum broadcast channel

We consider the problem of communication over a classical-quantum broadcast channel with one sender and two receivers. Generalizing the classical inner bounds shown by Marton and the recent quantum asymptotic version shown by Savov and Wilde, we obtain one-shot inner bounds in the quantum setting. Our bounds are stated in terms of smooth min and max Renyi divergences. We obtain these results using a different analysis of the random codebook argument and employ a new one-shot classical mutual covering argument based on rejection sampling. These results give a full justification of the claims of Savov and Wilde in the classical-quantum asymptotic iid setting; the techniques also yield similar bounds in the information spectrum setting.