Properties of subentropy

Abstract

Subentropy is an entropy-like quantity that arises in quantum information theory; for example, it provides a tight lower bound on the accessible information for pure state ensembles, dual to the von Neumann entropy upper bound in Holevo's theorem. Here we establish a series of properties of subentropy, paralleling the well-developed analogous theory for von Neumann entropy. Further, we show that subentropy is a lower bound for min-entropy. We introduce a notion of conditional subentropy and show that it can be used to provide an upper bound for the guessing probability of any classical-quantum state of two qubits; we conjecture that the bound applies also in higher dimensions. Finally we give an operational interpretation of subentropy within classical information theory.

15 pages

References in corpus (1)

• A Sharp Fannes-type Inequality for the von Neumann Entropy

Cited by in corpus (12)

• Quantum coherence and geometric quantum discord
• Complementarity relations for quantum coherence
• alpha-z-relative Renyi entropies
• A Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity
• Entropy power inequalities for qudits
• Average subentropy, coherence and entanglement of random mixed quantum states
• Average coherence and its typicality for random mixed quantum states
• Stabilizer Testing and Magic Entropy via Quantum Fourier Analysis
• Coherence-mixedness trade-offs
• Entropy, subentropy and the elementary symmetric functions
• Tradeoff relations between accessible information, informational power, and purity
• A classical interpretation of the Scrooge distribution