dorsal/arxiv
View SchemaDistilling common randomness from bipartite quantum states
| Authors | I. Devetak, A. Winter |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0304196 |
| URL | https://arxiv.org/abs/quant-ph/0304196 |
| DOI | 10.1109/TIT.2004.838115 |
| Journal | IEEE Trans. Inf. Theory 50(12):3183-3196, 2004 |
Abstract
The problem of converting noisy quantum correlations between two parties into noiseless classical ones using a limited amount of one-way classical communication is addressed. A single-letter formula for the optimal trade-off between the extracted common randomness and classical communication rate is obtained for the special case of classical-quantum correlations. The resulting curve is intimately related to the quantum compression with classical side information trade-off curve $Q^*(R)$ of Hayden, Jozsa and Winter. For a general initial state we obtain a similar result, with a single-letter formula, when we impose a tensor product restriction on the measurements performed by the sender; without this restriction the trade-off is given by the regularization of this function. Of particular interest is a quantity we call ``distillable common randomness'' of a state: the maximum overhead of the common randomness over the one-way classical communication if the latter is unbounded. It is an operational measure of (total) correlation in a quantum state. For classical-quantum correlations it is given by the Holevo mutual information of its associated ensemble, for pure states it is the entropy of entanglement. In general, it is given by an optimization problem over measurements and regularization; for the case of separable states we show that this can be single-letterized.
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"abstract": "The problem of converting noisy quantum correlations between two parties into\nnoiseless classical ones using a limited amount of one-way classical\ncommunication is addressed. A single-letter formula for the optimal trade-off\nbetween the extracted common randomness and classical communication rate is\nobtained for the special case of classical-quantum correlations. The resulting\ncurve is intimately related to the quantum compression with classical side\ninformation trade-off curve $Q^*(R)$ of Hayden, Jozsa and Winter. For a general\ninitial state we obtain a similar result, with a single-letter formula, when we\nimpose a tensor product restriction on the measurements performed by the\nsender; without this restriction the trade-off is given by the regularization\nof this function. Of particular interest is a quantity we call ``distillable\ncommon randomness\u0027\u0027 of a state: the maximum overhead of the common randomness\nover the one-way classical communication if the latter is unbounded. It is an\noperational measure of (total) correlation in a quantum state. For\nclassical-quantum correlations it is given by the Holevo mutual information of\nits associated ensemble, for pure states it is the entropy of entanglement. In\ngeneral, it is given by an optimization problem over measurements and\nregularization; for the case of separable states we show that this can be\nsingle-letterized.",
"arxiv_id": "quant-ph/0304196",
"authors": [
"I. Devetak",
"A. Winter"
],
"categories": [
"quant-ph"
],
"doi": "10.1109/TIT.2004.838115",
"journal_ref": "IEEE Trans. Inf. Theory 50(12):3183-3196, 2004",
"title": "Distilling common randomness from bipartite quantum states",
"url": "https://arxiv.org/abs/quant-ph/0304196"
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