Iterated stochastic measurements
Abstract
We describe a measurement device principle based on discrete iterations of Bayesian updating of systemstate probability distributions. Although purely classical by nature, these measurements are accompanied with a progressive collapse of the systemstate probability distribution during each complete system measurement. This measurement scheme finds applications in analysing repeated nondemolition 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's 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 Wu's 80th birthday.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 December 2012
 DOI:
 10.1088/17518113/45/49/494020
 arXiv:
 arXiv:1210.0425
 Bibcode:
 2012JPhA...45W4020B
 Keywords:

 Mathematical Physics;
 Condensed Matter  Statistical Mechanics;
 Mathematics  Probability
 EPrint:
 23 pages, 1 figure. To be published in J. Phys. A