Reliability Function of Classical-Quantum Channels
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 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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.12403
- arXiv:
- arXiv:2407.12403
- Bibcode:
- 2024arXiv240712403L
- Keywords:
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- Quantum Physics;
- Computer Science - Information Theory
- E-Print:
- Revised version, new style, 7 pages, no figures, minor issues fixed, references added. See also independent work arXiv:2407.11118 by Joseph M. Renes