Thursday, March 21, 2013

1303.4744 (Toby S. Cubitt et al.)

Stability of local quantum dissipative systems    [PDF]

Toby S. Cubitt, Angelo Lucia, Spyridon Michalakis, David Perez-Garcia
Open quantum systems weakly coupled to the environment are modelled by completely positive, trace preserving semigroups of linear maps. The generators of such evolutions are called Lindbladians. For practical and theoretical reasons, it is crucial to estimate the impact that noise or errors in the generating Lindbladian can have on the evolution. In the setting of quantum many-body systems on a lattice it is natural to consider local or exponentially decaying interactions. We show that in this case local observables and correlation functions are stable if the Lindbladian is frustration free, translational invariant (uniformly), has a unique fix point (with no restriction on its rank) and has a mixing time which scales logarithmically with the system size. These conditions can be relaxed to the non-translational invariant case, at the cost of requiring Local Topological Quantum Order. As a main example we prove that classical Glauber dynamics is stable under local perturbations, including perturbations in the transition rates which do not preserve detailed balance.
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