An Evolutionary Formalism for Weak Quantum Measurements

TL;DR

This paper introduces a new dynamical evolution equation for quantum state collapse during weak measurements, offering a potential alternative to the Born rule with testable experimental predictions.

Contribution

It proposes a novel formalism for the evolution of quantum states during weak measurements, extending the standard quantum mechanics framework.

Findings

Predictions differ from the Born rule in weak measurement regimes

The formalism is consistent with quantum mechanics axioms

Open question on experimental observability of differences

Abstract

Unitary evolution and projective measurement are fundamental axioms of quantum mechanics. Even though projective measurement yields one of the eigenstates of the measured operator as the outcome, there is no theory that predicts which eigenstate will be observed in which experimental run. There exists only an ensemble description, which predicts probabilities of various outcomes over many experimental runs. We propose a dynamical evolution equation for the projective collapse of the quantum state in individual experimental runs, which is consistent with the well-established framework of quantum mechanics. In case of gradual weak measurements, its predictions for ensemble evolution are different from those of the Born rule. It is an open question whether or not suitably designed experiments can observe this alternate evolution.