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Lieb-Robinson Bounds and the Generation of Correlations and Topological Quantum Order

Bravyi, S. and Hastings, M. B. and Verstraete, F. (2006) Lieb-Robinson Bounds and the Generation of Correlations and Topological Quantum Order. Physical Review Letters, 97 (5). Art. No. 050401. ISSN 0031-9007. doi:10.1103/PhysRevLett.97.050401.

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The Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light cone with exponentially decaying tails. We discuss several consequences of this result in the context of quantum information theory. First, we show that the information that leaks out to spacelike separated regions is negligible and that there is a finite speed at which correlations and entanglement can be distributed. Second, we discuss how these ideas can be used to prove lower bounds on the time it takes to convert states without topological quantum order to states with that property. Finally, we show that the rate at which entropy can be created in a block of spins scales like the boundary of that block.

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Additional Information:© 2006 The American Physical Society. (Received 10 April 2006; published 31 July 2006) S.B. was supported in part by National Science Foundation under Grant No. PHY99-07949, M.B.H. by U.S. DOE No. W-7405-ENG-36, and F.V. by the Gordon and Betty Moore Foundation through Caltech’s Center for the Physics of Information and the National Science Foundation under Grant No. PHY-0456720.
Funding AgencyGrant Number
National Science FoundationPHY99-07949
Department of EnergyW-7405-ENG-36
Gordon and Betty Moore FoundationUNSPECIFIED
Center for Physics of Information, CaltechUNSPECIFIED
National Science FoundationPHY-0456720
Issue or Number:5
Record Number:CaltechAUTHORS:BRAprl06
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12433
Deposited By: Archive Administrator
Deposited On:26 Nov 2008 19:09
Last Modified:08 Nov 2021 22:28

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