Reliability Function of Classical-Quantum Channels

• URL: http://arxiv.org/abs/2407.12403v4
• Date: Mon, 17 Feb 2025 09:04:54 GMT
• Title: Reliability Function of Classical-Quantum Channels
• Authors: Ke Li, Dong Yang,
• Abstract summary: We study the reliability function of general classical-quantum channels. We prove a lower bound, in terms of the quantum Renyi information in Petz's form, for the reliability function.
• Score: 6.959602244161659
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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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