Tristan Benoist

Repeated Quantum Non-Demolition Measurements: Convergence and Continuous Time Limit

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. We extend this result to mixed states and we prove similar results for the system density matrix. 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 behavior of these continuous time processes and prove convergence.

Iterated stochastic measurements

We describe a measurement device principle based on discrete iterations of Bayesian updating of system-state probability distributions. Although purely classical by nature, these measurements are accompanied with a progressive collapse of the system-state probability distribution during each complete system measurement. This measurement scheme finds applications in analysing repeated non-demolition indirect quantum measurements. We also analyse the continuous time limit of these processes, either in the Brownian diffusive limit or in the Poissonian jumpy limit. In the quantum mechanical framework, this continuous time limit leads to Belavkins equations which describe quantum systems under continuous measurements.This article is part of ?Lattice models and integrability?, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wus 80th birthday.

Large Time Behavior and Convergence Rate for Quantum Filters Under Standard Non Demolition Conditions

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Exponential Stability of Subspaces for Quantum Stochastic Master Equations

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Invariant Measure for Quantum Trajectories

S undergoing continuous time measurement is usually described by a jump-diffusion stochastic differential equation. Such an equation is called a quantum filtering equation (or quantum stochastic master equation) and its solution is called a quantum filter (or quantum trajectory). This solution describes the evolution of the state of

Energy Conservation and Full Counting Statistics

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