Rényi-Holevo inequality from $\alpha$-$z$-Rényi relative entropies

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 $\alpha$-$z$-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 $\alpha$-mutual information, suggesting new insights into communication channel performance and the fundamental limits for reliability functions in memoryless multi-letter communication channels.

References in corpus (11)

• Rényi Divergence and Kullback-Leibler Divergence
• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• From Classical to Quantum Shannon Theory
• alpha-z-relative Renyi entropies
• Robustness of Measurement, discrimination games and accessible information
• Generalized relative entropies and the capacity of classical-quantum channels
• From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture (New title)
• Investigating Properties of a Family of Quantum Renyi Divergences
• Equality conditions of Data Processing Inequality for $\alpha$-$z$ Rényi relative entropies
• Generalized approach to quantify correlations in bipartite quantum systems
• Generalized Holevo theorem and distinguishability notions