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Properties of subentropy
6. S. Nichols and W. Wootters, “Between entropy and subentropy,” Quant. Inf. Comput 3, 14 (2003).
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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.
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