Repeated quantum non-demolition measurements: convergence and continuous-time limit

Abstract

We analyze general enough models of repeated indirect measurements in which a quantum system interacts repeatedly with randomly chosen probes on which Von Neumann direct measurements are performed. We prove, under suitable hypotheses, that the system state probability distribution converges after a large number of repeated indirect measurements, in a way compatible with quantum wave function collapse. Similarly a modified version of the system density matrix converges. We show that the convergence is exponential with a rate given by some relevant mean relative entropies. We also prove that, under appropriate rescaling of the system and probe interactions, the state probability distribution and the system density matrix are solutions of stochastic differential equations modeling continuous-time quantum measurements. We analyze the large time convergence of these continuous-time processes and prove convergence.

44 pages, no figure

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Cited by in corpus (17)

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• On entropy production of repeated quantum measurements I. General theory
• Large Time Behaviour and Convergence Rate for Non Demolition Quantum Trajectories
• On bipartite unitary matrices generating subalgebra-preserving quantum operations
• Stability of continuous-time quantum filters with measurement imperfections
• On entropy production of repeated quantum measurements II. Examples
• The appearance of particle tracks in detectors
• Entanglement of Bipartite Quantum Systems driven by Repeated Interactions
• Concentration Inequalities for Output Statistics of Quantum Markov Processes
• Emergence of jumps in quantum trajectories via homogeneization
• Linear response theory and entropic fluctuations in repeated interaction quantum systems
• On stability of quantum trajectories and their Cesaro mean
• Digital homodyne and heterodyne detection for stationary bosonic modes
• Quantum Repeated Interactions and the Chaos Game
• Quantum model reduction for continuous-time quantum filters
• Quantum Measurements of Scattered Particles
• Asymptotic Purification of Quantum Trajectories under Random Generalized Measurements