While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the monotonicity theorem for relative entropies many bounds on the classical information extracted in a quantum measurement are obtained in a unified manner. In particular, it is shown that such bounds can all be stated as inequalities between mutual entropies. This approach based on channels gives rise to a unified picture of known and new bounds on the classical information (the bounds by Holevo, by Shumacher, Westmoreland and Wootters, by Hall, by Scutaru, a new upper bound and a new lower one). Some examples clarify the mutual relationships among the various bounds.

Quantum measurements and entropic bounds on information transmission / A. Barchielli, G.Lupieri. - In: QUANTUM INFORMATION & COMPUTATION. - ISSN 1533-7146. - 6:1(2006), pp. 016-045.

### Quantum measurements and entropic bounds on information transmission

#### Abstract

While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the monotonicity theorem for relative entropies many bounds on the classical information extracted in a quantum measurement are obtained in a unified manner. In particular, it is shown that such bounds can all be stated as inequalities between mutual entropies. This approach based on channels gives rise to a unified picture of known and new bounds on the classical information (the bounds by Holevo, by Shumacher, Westmoreland and Wootters, by Hall, by Scutaru, a new upper bound and a new lower one). Some examples clarify the mutual relationships among the various bounds.
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Instrument, Channel, Quantum Information, Entropy, Mutual Entropy Holevo bound
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2434/17263`
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