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arXiv · 2309.04539

R\'enyi-Holevo inequality from $\alpha$-$z$-R\'enyi relative entropies

Diego G. Bussandri·Grzegorz Rajchel-Mieldzioć·Pedro W. Lamberti·Karol Życzkowski
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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 $\alpha$-$z$-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 $\alpha$-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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Diego G. Bussandri, Grzegorz Rajchel-Mieldzioć, Pedro W. Lamberti, Karol Życzkowski. 2023-09-08. R\'enyi-Holevo inequality from $\alpha$-$z$-R\'enyi relative entropies. https://doi.org/10.1142/s021974992440015x

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