TY - JOUR
T1 - Distilling common randomness from bipartite quantum states
AU - Devetak, Igor
AU - Winter, Andreas
N1 - Funding Information:
Manuscript received May 16, 2003; revised April 9, 2004. The work of I. Devetak was supported in part by the National Science Foundation under the U.S. Army Research Office (ARO), Grants DAAG55-98-C-0041 and DAAD19-01-1-06. The work of A. Winter was supported by the U.K. Engineering and Physical Sciences Research Council. I. Devetak is with the IBM T. J. Watson Research Center, Yorktown Heights, NY 10598 USA (e-mail: [email protected]). A. Winter is with the Department of Mathematics, University of Bristol, Bristol BS8 1UB, U.K. (e-mail: [email protected]). Communicated by E. Knill, Associate Editor for Quantum Information Theory. Digital Object Identifier 10.1109/TIT.2004.838115
PY - 2004/12
Y1 - 2004/12
N2 - 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.
AB - 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.
KW - Additivity
KW - Common randomness
KW - Quantum theory
KW - Tradeoff
UR - http://www.scopus.com/inward/record.url?scp=10644254545&partnerID=8YFLogxK
U2 - 10.1109/TIT.2004.838115
DO - 10.1109/TIT.2004.838115
M3 - Article
AN - SCOPUS:10644254545
SN - 0018-9448
VL - 50
SP - 3183
EP - 3196
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 12
ER -