Decompositions of Hilbert Spaces, Stability Analysis and Convergence Probabilities for Discrete-Time Quantum Dynamical Semigroups

Abstract

We investigate convergence properties of discrete-time semigroup quantum dynamics, including asymptotic stability, probability and speed of convergence to pure states and subspaces. These properties are of interest in both the analysis of uncontrolled evolutions and the engineering of controlled dynamics for quantum information processing. Our results include two Hilbert space decompositions that allow for deciding the stability of the subspace of interest and for estimating of the speed of convergence, as well as a formula to obtain the limit probability distribution for a set of orthogonal invariant subspaces.

arXiv comment14 pages, no figures, to appear in Journal of Physics A, 2015

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Cited by in corpus (13)

• Geometry and response of Lindbladians
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• Exponential Stability of Subspaces for Quantum Stochastic Master Equations
• Estimating the decoherence time using non-commutative Functional Inequalities
• Quantized recurrence time in iterated open quantum dynamics
• Asymptotics of quantum channels
• Symmetrizing quantum dynamics beyond gossip-type algorithms
• Strict Positivity and $D$-Majorization
• Lindbladians with multiple steady states: theory and applications
• Asymptotic Dynamics of Open Quantum Systems and Modular Theory
• From independent sets and vertex colorings to isotropic spaces and isotropic decompositions
• Alternating Projections Methods for Discrete-time Stabilization of Quantum States
• Model Checking Quantum Continuous-Time Markov Chains