Continuity of measurement outcomes

TL;DR

This paper shows that the collapse of the wave function is equivalent to the continuity of measurement outcomes, providing a unified view applicable to both quantum and classical physics and highlighting quantum coherences as the key factor in deviations.

Contribution

It introduces a continuity-based approach to the measurement problem that applies to both quantum and classical physics, enabling comparison and quantification of quantum features.

Findings

Quantum coherences cause measurable deviations in statistical properties.

The continuity requirement applies to classical physics as well as quantum.

The approach allows characterization of quantum measurement features within resource theories.

Abstract

It is demonstrated that the collapse of the wave function is equivalent to the continuity of measurement outcomes. The latter states that a second measurement has to result in the same outcome as the first measurement of the same observable for a vanishing time between both observations. In contrast to the exclusively quantum-physical collapse description, the equivalent continuity requirement also applies in classical physics, allowing for a comparison of both domains. In particular, it is found that quantum coherences are the single cause for measurable deviations in statistical properties due to the collapse. Therefore, the introduced approach renders it possible to characterize and quantify the unique features of the quantum-physical measurement problem within the framework of modern quantum resource theories and compare them to classical physics.