### 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 tradeoff 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 tradeoff 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 tradeoff 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 singleletterized.

Translated title of the contribution | Distilling common randomness from bipartite quantum states |
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Original language | English |

Pages (from-to) | 3183 - 3196 |

Journal | IEEE Transactions on Information Theory |

Volume | 50 (12) |

Publication status | Published - Dec 2004 |

### Bibliographical note

Publisher: IEEE-Inst Electrical Electronic Engineers IncOther identifier: IDS Number: 874PT

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## Cite this

Devetak, I., & Winter, AJ. (2004). Distilling common randomness from bipartite quantum states.

*IEEE Transactions on Information Theory*,*50 (12)*, 3183 - 3196.