Indirect retrieval of information and the emergence of facts in quantum mechanics

TL;DR

This paper develops a mathematical framework for indirect and non-demolition measurements in quantum mechanics, showing how sequences of simple observations can reveal precise information about complex quantum observables.

Contribution

It introduces novel mathematical tools and concepts from classical probability theory to formalize and analyze indirect measurement processes in quantum systems.

Findings

Sequences of simple measurements can accurately infer complex quantum observables

Mathematical tools like the algebra of functions measurable at infinity are applied to quantum measurement theory

The approach links quantum measurement with classical probability concepts such as the Central Limit Theorem

Abstract

Long sequences of successive direct (projective) measurements or observations of a few "uninteresting" physical quantities of a quantum system may reveal indirect, but precise and unambiguous information on the values of some very "interesting" observables of the system. In this paper, the mathematics underlying this claim is developed; i.e., we attempt to contribute to a mathematical theory of indirect and, in particular, non-demolition measurements in quantum mechanics. Our attempt leads us to make novel uses of classical notions and results of probability theory, such as the "algebra of functions measurable at infinity", the Central Limit Theorem, results concerning relative entropy and its role in the theory of large deviations, etc.