A non-probabilistic substitute for the Born rule

TL;DR

This paper introduces a non-probabilistic framework for quantum measurement outcomes, replacing the Born rule with two postulates that focus on state overlap and robustness, aligning with standard interpretations.

Contribution

It proposes a novel non-probabilistic approach to quantum measurement, avoiding the interpretational issues of the Born rule by using two simple postulates.

Findings

Retrieves standard interpretations of the Born rule

Provides a non-probabilistic foundation for quantum measurement

Ensures robustness of observed outcomes under small perturbations

Abstract

The Born rule assigns a probability to any possible outcome of a quantum measurement, but leaves open the question how these probabilities are to be interpreted and, in particular, how they relate to the outcome observed in an actual experiment. We propose to avoid this question by replacing the Born rule with two non-probabilistic postulates: (i) the projector associated to the observed outcome must have a positive overlap with the state of the measured system; (ii) statements about observed outcomes are robust, that is, remain valid under small perturbations of the state. We show that the two postulates suffice to retrieve the interpretations of the Born rule that are commonly used for analysing experimental data.