Properties of subentropy

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 sub...

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Bibliographic Details
Published in:Journal of mathematical physics 2014-06, Vol.55 (6), p.1
Main Authors: Datta, Nilanjana, Dorlas, Tony, Jozsa, Richard, Benatti, Fabio
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Dimensional analysis
ENTROPY
INFORMATION THEORY
Lower bounds
Physics
Probability
PURE STATES
QUANTUM MECHANICS
QUANTUM OPERATORS
Quantum phenomena
Quantum physics
Quantum theory
QUBITS
Qubits (quantum computing)
Theorems
Upper bounds
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Summary: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.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4882935