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On quantum Renyi entropies: a new generalization and some properties
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The Renyi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or mutual information, and have found many applications in information theory and beyond. Various generalizations of Renyi entropies to the quantum setting have been proposed, most notably Petz's quasi-entropies and Renner's conditional min-, max- and collision entropy. Here, we argue that previous quantum extensions are incompatible and thus unsatisfactory. We propose a new quantum generalization of the family of Renyi entropies that contains the von Neumann entropy, min-entropy, collision entropy and the max-entropy as special cases, thus encompassing most quantum entropies in use today. We show several natural properties for this definition, including data-processing inequalities, a duality relation, and an entropic uncertainty relation.
Forward citations
Cited by 4 Pith papers
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A general proof of integer R\'enyi QNEC
Proves integer Rényi QNEC by establishing log-convexity of Kosaki L^n norms under null-translation semigroups for σ-finite von Neumann algebras with half-sided modular inclusions, assuming only finite sandwiched Rényi...
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Finite-size quantum key distribution rates from R\'enyi entropies using conic optimization
A general conic optimization solver computes finite-size QKD rates from Rényi entropies more reliably than prior Frank-Wolfe methods.
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R\'enyi divergences and binary state discrimination error exponents for fermionic quasi-free states
Explicit formulas are given for regularized Rényi divergences of several kinds between fermionic quasifree states, with all types coinciding in the single-mode case and remaining distinct for multiple modes per site.
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Constrained free energy minimization for the design of thermal states and stabilizer thermodynamic systems
Benchmarks gradient-ascent algorithms for constrained free energy minimization on quantum Heisenberg models and stabilizer codes, with applications to thermal state design and fixed-temperature quantum encoding.
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