Stability of local quantum dissipative systems
arXiv:1303.4744 · doi:10.1007/s00220-015-2355-3
Abstract
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 which 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.
38 pages, 3 figures. Final version
References in corpus (9)
- Non-Abelian Anyons and Topological Quantum Computation
- Local stabilizer codes in three dimensions without string logical operators
- Experimental multiparticle entanglement dynamics induced by decoherence
- Quantum memories based on engineered dissipation
- Quantum logarithmic Sobolev inequalities and rapid mixing
- Hypercontractivity of quasi-free quantum semigroups
- Spectral convergence bounds for classical and quantum Markov processes
- Perturbation Bounds for Quantum Markov Processes and their Fixed Points
- Generating topological order: no speedup by dissipation
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