Lower Bounds on Error Exponents via a New Quantum Decoder

We introduce a new quantum decoder based on a variant of the pretty good measurement, but defined via an alternative matrix quotient. We then use this novel decoder to derive new lower bounds on the error exponent both in the one-shot and asymptotic regimes for the classical-quantum and the entanglement-assisted channel coding problems. Our bounds are expressed in terms of measured (for the one-shot bounds) and sandwiched (for the asymptotic bounds) channel Rényi mutual information of order between 1/2 and 1. The bounds are not comparable with some previously established bounds for general channels, yet they are tight (for rates close to capacity) when the channel is classical. Finally, we also use our new decoder to rederive Cheng’s recent tight bound on the decoding error probability, which implies that most existing asymptotic results also hold for the new decoder.