On quantum conditional entropies defined in terms of the $f$-divergences

Abstract

We consider a family of quantum conditional entropies based on the concept of quantum $f$-divergences. First, we explicitly formulate conditions under which the notion of quantum conditional entropy is well defined in this way. In particular, we demand that the value of conditional entropy be independent of any extension of the principal Hilbert space. Using fundamental properties of the quantum $f$-divergences, several interesting relations for such conditional entropies are formulated. We separately examine an especially important case of quantum conditional entropies related to the Tsallis divergence.

13 pages, no figures. The paper is substantially revised

References in corpus (8)

• On quantum Renyi entropies: a new generalization and some properties
• Sandwiched Rényi Divergence Satisfies Data Processing Inequality
• Monotonicity of a relative Rényi entropy
• Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies
• Smooth Max-Information as One-Shot Generalization for Mutual Information
• Strong converse for the classical capacity of the pure-loss bosonic channel
• From the sandwiched quantum relative Tsallis entropy to its conditional form: Separability criterion beyond local and global spectra
• Generalized conditional entropy in bipartite quantum systems

Cited by in corpus (1)

• Quantum Correlation with Sandwiched Relative Entropies: Advantageous as Order Parameter in Quantum Phase Transitions