Distilling common randomness from bipartite quantum states

Igor Devetak, Andreas Winter

Research output: Contribution to journalArticlepeer-review

83 Scopus citations


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 single-letterized.

Original languageEnglish
Pages (from-to)3183-3196
Number of pages14
JournalIEEE Transactions on Information Theory
Issue number12
StatePublished - Dec 2004
Externally publishedYes


  • Additivity
  • Common randomness
  • Quantum theory
  • Tradeoff


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