We present a new decoding protocol to realize transmission of classical information through a quantum channel at asymptotically maximum capacity, achieving the Holevo bound and thus the optimal communication rate. At variance with previous proposals, our scheme recovers the message bit by bit, making use of a series of “yes-no” measurements, organized in bisection fashion, thus determining which codeword was sent in log2 N steps, N being the number of codewords.
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The code average in the first two properties can be removed when using a stronger notion of conditional typicality, which we do not state here for simplicity, since such average will appear quite naturally during calculations when making use of Shannon’s averaging trick.
An alternative computation of the error probability can be carried out by employing a generalization of Sen’s non-commutative union bound,30 obtaining the same condition on the single-step POVM for the optimality of the bisection protocol.
