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arXiv · 2407.12403

Reliability Function of Classical-Quantum Channels

Ke Li·Dong Yang
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Abstract

We study the reliability function of general classical-quantum channels, which describes the optimal exponent of the decay of decoding error when the communication rate is below the capacity. As the main result, we prove a lower bound, in terms of the quantum Renyi information in Petz's form, for the reliability function. This resolves Holevo's conjecture proposed in 2000, a long-standing open problem in quantum information theory. It turns out that the obtained lower bound matches the upper bound derived by Dalai in 2013, when the communication rate is above a critical value. Thus, we have determined the reliability function in this high-rate case. Our approach relies on Renes' breakthrough made in 2022, which relates classical-quantum channel coding to that of privacy amplification, as well as our new characterization of the channel Renyi information.

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Ke Li, Dong Yang. 2024-07-17. Reliability Function of Classical-Quantum Channels. https://doi.org/10.1103/physrevlett.134.010802

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