Renyi-Holevo Inequality from ?- z -Renyi Relative Entropies

Articulo

Authorship:

Bussandri, Diego ; Rajchel Mieldzioc, Grzegorz ; LAMBERTI, PEDRO WALTER ; Zyczkowski, Karol

Date:

2024

Publishing House and Editing Place:

WORLD SCIENTIFIC PUBL CO PTE LTD

Magazine:

INTERNATIONAL JOURNAL OF QUANTUM INFORMATION (pp. 1-14) WORLD SCIENTIFIC PUBL CO PTE LTD

Summary

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 ?-z-R´enyi relative entropies, which comprise known relevant quantities such as the R´enyi relative entropy and the sandwiched R´enyi relative entropy, we establish the Holevo-R´enyi 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.

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http://hdl.handle.net/11336/238964