Rényi–Holevo inequality from α-z-Rényi relative entropies

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Abstract
We investigate bounds in the transmission of classical information through quantum systems. Our focus lies in the generalized Holevo theorem, which provides a single-letter Holevo-like inequality from arbitrary quantum distance measures. Through the introduction of the [ ]-[ ]-Rényi relative entropies, which comprise known relevant quantities such as the Rényi relative entropy and the sandwiched Rényi relative entropy, we establish the Holevo–Rényi inequality. This result leads to a quantum bound for the [ ]-mutual information, suggesting new insights into communication channel performance and the fundamental limits for reliability functions in memoryless multi-letter communication channels.
Funding Information
  • MCIN (PID2020-113406GB-I00)
  • MCIN (RED2022-134301-T)
  • Narodowe Centrum Nauki under the Quantera (2021/03/Y/ST2/00193)

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