A bound on the mutual information, and properties of entropy reduction, for quantum channels with inefficient measurements

Abstract

The Holevo bound is a bound on the mutual information for a given quantum encoding. In 1996 Schumacher, Westmoreland and Wootters [Schumacher, Westmoreland and Wootters, Phys. Rev. Lett. 76, 3452 (1996)] derived a bound which reduces to the Holevo bound for complete measurements, but which is tighter for incomplete measurements. The most general quantum operations may be both incomplete and inefficient. Here we show that the bound derived by SWW can be further extended to obtain one which is yet again tighter for inefficient measurements. This allows us in addition to obtain a generalization of a bound derived by Hall, and to show that the average reduction in the von Neumann entropy during a quantum operation is concave in the initial state, for all quantum operations. This is a quantum version of the concavity of the mutual information. We also show that both this average entropy reduction, and the mutual information for pure state ensembles, are Schur-concave for unitarily covariant measurements; that is, for these measurements, information gain increases with initial uncertainty.

7 pages, revtex4. v2: published version; note added regarding similar work by Barchielli and Lupieri

References in corpus (4)

• Separable states are more disordered globally than locally
• Quantum Operations, State Transformations and Probabilities
• Information-disturbance tradeoff in quantum measurement on the uniform ensemble and on the mutually unbiased bases
• Efficient measurements, purification, and bounds on the mutual information

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• Identifying the Information Gain of a Quantum Measurement
• Entropy reduction of quantum measurements
• Quantum process inference for a single qubit Maxwell's demon
• Necessity of Feedback Control for the Quantum Maxwell Demon in a Finite-Time Steady Feedback Cycle