Iterated Stochastic Measurements

Abstract

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 Belavkin equations which describe quantum systems under continuous measurements.

23 pages, 1 figure. To be published in J. Phys. A

References in corpus (2)

• Progressive field-state collapse and quantum non-demolition photon counting
• Existence, uniqueness and approximation of a stochastic Schrödinger equation: the diffusive case

Cited by in corpus (9)

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• Emergence of jumps in quantum trajectories via homogeneization
• Real time imaging of quantum and thermal fluctuations: the case of a two-level system
• On stability of quantum trajectories and their Cesaro mean
• Digital homodyne and heterodyne detection for stationary bosonic modes
• Quantum Metrology via Repeated Quantum Nondemolition Measurements in "Photon Box"