dorsal/arxiv
View SchemaA bound on the mutual information, and properties of entropy reduction, for quantum channels with inefficient measurements
| Authors | Kurt Jacobs |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0412006 |
| URL | https://arxiv.org/abs/quant-ph/0412006 |
| DOI | 10.1063/1.2158433 |
| Journal | J. Math. Phys. 47, 012102 (2006) |
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.
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"abstract": "The Holevo bound is a bound on the mutual information for a given quantum\nencoding. In 1996 Schumacher, Westmoreland and Wootters [Schumacher,\nWestmoreland and Wootters, Phys. Rev. Lett. 76, 3452 (1996)] derived a bound\nwhich reduces to the Holevo bound for complete measurements, but which is\ntighter for incomplete measurements. The most general quantum operations may be\nboth incomplete and inefficient. Here we show that the bound derived by SWW can\nbe further extended to obtain one which is yet again tighter for inefficient\nmeasurements. This allows us in addition to obtain a generalization of a bound\nderived by Hall, and to show that the average reduction in the von Neumann\nentropy during a quantum operation is concave in the initial state, for all\nquantum operations. This is a quantum version of the concavity of the mutual\ninformation. We also show that both this average entropy reduction, and the\nmutual information for pure state ensembles, are Schur-concave for unitarily\ncovariant measurements; that is, for these measurements, information gain\nincreases with initial uncertainty.",
"arxiv_id": "quant-ph/0412006",
"authors": [
"Kurt Jacobs"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.2158433",
"journal_ref": "J. Math. Phys. 47, 012102 (2006)",
"title": "A bound on the mutual information, and properties of entropy reduction, for quantum channels with inefficient measurements",
"url": "https://arxiv.org/abs/quant-ph/0412006"
},
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