Measurement theory for closed quantum systems

TL;DR

This paper develops a measurement theory for closed quantum systems by defining classical observables with minimal quantum fluctuations, offering insights into the quantum measurement problem without relying on environmental interactions.

Contribution

It introduces a novel concept of classical observables for closed systems and links them to the quantum measurement problem, bypassing the need for environment-based explanations.

Findings

Classical observables can be constructed for time-evolved pure states.

The approach identifies Schrödinger cats intrinsically.

Provides a new perspective on the quantum measurement problem.

Abstract

We introduce the concept of a "classical observable" as an operator with vanishingly small quantum fluctuations on a set of density matrices. It is shown how to construct them for a time evolved pure state. The study of classical observables provides a natural starting point to analyse the quantum measurement problem. In particular, it allows to identify Schr\"odinger cats and the associated projection operators intrinsically, without the need to invoke an environment. We discuss how our new approach relates to the open system analysis of the quantum measurement problem.