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Stability of Local Quantum Dissipative Systems

Cubitt, Toby S. and Lucia, Angelo and Michalakis, Spyridon and Pérez-García, David (2015) Stability of Local Quantum Dissipative Systems. Communications in Mathematical Physics, 337 (3). pp. 1275-1315. ISSN 0010-3616. doi:10.1007/s00220-015-2355-3.

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Open quantum systems weakly coupled to the environment are modeled by completely positive, trace preserving semigroups of linear maps. The generators of such evolutions are called Lindbladians. In the setting of quantum many-body systems on a lattice it is natural to consider Lindbladians that decompose into a sum of local interactions with decreasing strength with respect to the size of their support. For both practical and theoretical reasons, it is crucial to estimate the impact that perturbations in the generating Lindbladian, arising as noise or errors, can have on the evolution. These local perturbations are potentially unbounded, but constrained to respect the underlying lattice structure. We show that even for polynomially decaying errors in the Lindbladian, local observables and correlation functions are stable if the unperturbed Lindbladian has a unique fixed point and a mixing time that scales logarithmically with the system size. The proof relies on Lieb–Robinson bounds, which describe a finite group velocity for propagation of information in local systems. As a main example, we prove that classical Glauber dynamics is stable under local perturbations, including perturbations in the transition rates, which may not preserve detailed balance.

Item Type:Article
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URLURL TypeDescription Paper ReadCube access
Lucia, Angelo0000-0003-1709-1220
Michalakis, Spyridon0000-0003-4963-1156
Pérez-García, David0000-0003-2990-791X
Additional Information:© 2015 Springer-Verlag Berlin Heidelberg. Received: 23 June 2014. Accepted: 15 January 2015. Published online: 7 April 2015. T.S.C. is supported by a Royal Society University Research fellowship, and was previously supported by a Juan de la Cierva fellowship. T.S.C., A.L., and D.P.-G. are supported by Spanish Grants MTM2011-26912 and QUITEMAD, and European CHIST-ERA project CQC (funded partially by MINECO Grant PRI-PIMCHI-2011-1071). A.L. is supported by Spanish Ministerio de Economía y Competividad FPI fellowship BES-2012-052404. S.M. acknowledges funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through Grant #GBMF1250 and by the AFOSR Grant #FA8750-12-2-0308. The authors would like to thank the hospitality of the Centro de Ciencias Pedro Pascual in Benasque, where part of this work was carried out. Communicated by M. M. Wolf.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Royal Society University Research fellowshipUNSPECIFIED
Juan de la Cierva fellowshipUNSPECIFIED
Spanish GrantMTM2011-26912
Ministerio de Economía y Competitividad (MINECO)PRI-PIMCHI-2011-1071
Ministerio de Economía y Competitividad (MINECO)BES-2012-052404
Institute for Quantum Information and MatterUNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationGBMF1250
Air Force Office of Scientific Research (AFOSR)FA8750-12-2-0308
Issue or Number:3
Record Number:CaltechAUTHORS:20150518-114234895
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:57603
Deposited By: Ruth Sustaita
Deposited On:18 May 2015 19:13
Last Modified:10 Nov 2021 21:52

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