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Aspects of Generic Entanglement

Hayden, Patrick and Leung, Debbie W. and Winter, Andreas (2006) Aspects of Generic Entanglement. Communications in Mathematical Physics, 265 (1). pp. 95-117. ISSN 0010-3616.

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We study entanglement and other correlation properties of random states in high-dimensional bipartite systems. These correlations are quantified by parameters that are subject to the "concentration of measure" phenomenon, meaning that on a large-probability set these parameters are close to their expectation. For the entropy of entanglement, this has the counterintuitive consequence that there exist large subspaces in which all pure states are close to maximally entangled. This, in turn, implies the existence of mixed states with entanglement of formation near that of a maximally entangled state, but with negligible quantum mutual information and, therefore, negligible distillable entanglement, secret key, and common randomness. It also implies a very strong locking effect for the entanglement of formation: its value can jump from maximal to near zero by tracing over a number of qubits negligible compared to the size of the total system. Furthermore, such properties are generic. Similar phenomena are observed for random multiparty states, leading us to speculate on the possibility that the theory of entanglement is much simplified when restricted to asymptotically generic states. Further consequences of our results include a complete derandomization of the protocol for universal superdense coding of quantum states.

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Additional Information:© 2006 Springer-Verlag. Received: 10 June 2005; Accepted: 28 September 2005; Published online: 3 March 2006. Communicated by M. B. Ruskai. Thanks to Noah Linden for interesting conversations on multiparty entangled states and for comments on an earlier version of our manuscript. A large part of this work was done during a visit of AW’s to the Institute for Quantum Information in spring 2004. AW gratefully acknowledges the hospitality of IQI during this time; he furthermore acknowledges support from the EU under European Commission project RESQ, contract No. IST-2001-37559. DL and PH are supported by National Science Foundation Grant No. EIA-0086038. PH acknowledges support from the Sherman Fairchild Foundation.
Funding AgencyGrant Number
European Union (EU)IST-2001-37559
Sherman Fairchild FoundationUNSPECIFIED
Subject Keywords:Keywords: entanglement, concentration of measure, superdense coding
Issue or Number:1
Classification Code:PACS: 03.65.Ta, 03.67.Hk
Record Number:CaltechAUTHORS:20110630-103235167
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Official Citation:Hayden, P., Leung, D. & Winter, A. Commun. Math. Phys. (2006) 265: 95.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:24268
Deposited By: Ruth Sustaita
Deposited On:30 Jun 2011 18:15
Last Modified:03 Oct 2019 02:54

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