Iterated Stochastic Measurements

TL;DR

This paper introduces a classical measurement scheme based on iterative Bayesian updates, which models continuous quantum measurements and their effects on system state probabilities, connecting to Belavkin equations.

Contribution

It presents a novel classical measurement approach that mimics quantum continuous measurements and derives its continuous time limits leading to Belavkin equations.

Findings

The measurement scheme demonstrates a progressive collapse of probability distributions.

Continuous time limits yield Belavkin equations for quantum systems.

The approach bridges classical Bayesian updates with quantum measurement theory.

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.