dorsal/arxiv
View SchemaQuantum measurements and entropic bounds on information transmission
| Authors | Alberto Barchielli, Giancarlo Lupieri |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0505090 |
| URL | https://arxiv.org/abs/quant-ph/0505090 |
| Journal | Quantum Information and Computation 6 (2006) 16-45 |
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 (Holevo's, Shumacher-Westmoreland-Wootters', Hall's, Scutaru's bounds, a new upper bound and a new lower one). Some examples clarify the mutual relationships among the various bounds.
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"abstract": "While a positive operator valued measure gives the probabilities in a quantum\nmeasurement, an instrument gives both the probabilities and the a posteriori\nstates. By interpreting the instrument as a quantum channel and by using the\nmonotonicity theorem for relative entropies many bounds on the classical\ninformation extracted in a quantum measurement are obtained in a unified\nmanner. In particular, it is shown that such bounds can all be stated as\ninequalities between mutual entropies. This approach based on channels gives\nrise to a unified picture of known and new bounds on the classical information\n(Holevo\u0027s, Shumacher-Westmoreland-Wootters\u0027, Hall\u0027s, Scutaru\u0027s bounds, a new\nupper bound and a new lower one). Some examples clarify the mutual\nrelationships among the various bounds.",
"arxiv_id": "quant-ph/0505090",
"authors": [
"Alberto Barchielli",
"Giancarlo Lupieri"
],
"categories": [
"quant-ph"
],
"journal_ref": "Quantum Information and Computation 6 (2006) 16-45",
"title": "Quantum measurements and entropic bounds on information transmission",
"url": "https://arxiv.org/abs/quant-ph/0505090"
},
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