Convergence of repeated quantum non-demolition measurements and wave function collapse

TL;DR

This paper rigorously proves that repeated indirect quantum non-demolition measurements lead to wave function collapse, linking the convergence rate to measurement information content, thus bridging quantum measurement theory and information theory.

Contribution

It provides a rigorous mathematical proof of wave function collapse via repeated QND measurements and relates the convergence rate to the relative entropy of measurements.

Findings

Repeated QND measurements converge to wave function collapse

The convergence rate is proportional to the relative entropy of measurements

Connects quantum measurement process with information theory principles

Abstract

Motivated by recent experiments on quantum trapped fields, we give a rigorous proof that repeated indirect quantum non-demolition (QND) measurements converge to the collapse of the wave function as predicted by the postulates of quantum mechanics for direct measurements. We also relate the rate of convergence toward the collapsed wave function to the relative entropy of each indirect measurement, a result which makes contact with information theory.