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The entanglement of purification

Terhal, Barbara M. and Horodecki, Michal and Leung, Debbie W. and DiVincenzo, David P. (2002) The entanglement of purification. Journal of Mathematical Physics, 43 (9). pp. 4286-4298. ISSN 0022-2488. doi:10.1063/1.1498001.

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We introduce a measure of both quantum as well as classical correlations in a quantum state, the entanglement of purification. We show that the (regularized) entanglement of purification is equal to the entanglement cost of creating a state rho asymptotically from maximally entangled states, with negligible communication. We prove that the classical mutual information and the quantum mutual information divided by two are lower bounds for the regularized entanglement of purification. We present numerical results of the entanglement of purification for Werner states in H(2)circle times H(2).

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Additional Information:© 2002 American Institute of Physics. Received 6 February 2002; accepted 16 May 2002. B.M.T., D.W.L., and D.P.D. are grateful for the support of the National Security Agency and the Advanced Research and Development Activity through Army Research Office Contract Nos DAAG55-98-C-0041 and DAAD19-01-C-0056 and partial support from the National Reconnaissance Office. This work was also supported in part by the National Science Foundation under Grant. No. EIA-0086038. M.H. acknowledges the support of EU grant EQUIP, Contract No. IST-1999-11053. We thank Charles Bennett, Paweł Horodecki, Ryszard Horodecki and John Smolin for a pleasant IBM lunch discussion on this topic. The concept of entanglement of purification was raised in a discussion of M.H. with Ryszard Horodecki. M.H. would also like to thank Robert Alicki and Ryszard Horodecki for stimulating discussions. B.M.T. would like to thank Andreas Winter for interesting discussions about the secret key rate K and its relation to other correlation measures. D.W.L. would like to thank Charles Bennett and John Smolin for discussions on mixed state inputs that violate Eq. (33).
Subject Keywords:quantum theory; quantum interference phenomena
Issue or Number:9
Record Number:CaltechAUTHORS:TERjmp02
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2190
Deposited By: Tony Diaz
Deposited On:14 Mar 2006
Last Modified:08 Nov 2021 19:45

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