Quantum probabilities from combination of Zurek's envariance and Gleason's theorem

TL;DR

This paper derives the quantum probability rule (Born rule) by combining Zurek's envariance concept with Gleason's theorem, offering a foundational perspective on quantum measurement probabilities.

Contribution

It presents a novel derivation of the quantum probability rule using environment-assisted invariance and Gleason's theorem, unifying two key ideas in quantum foundations.

Findings

Derivation of the Born rule from envariance and Gleason's theorem

Provides a new conceptual foundation for quantum probabilities

Shows the generality of the probability rule for POVMs

Abstract

The quantum-mechanical rule for probabilities, in its most general form of positive-operator valued measure (POVM), is shown to be a consequence of the environment-assisted invariance (envariance) idea suggested by Zurek [Phys. Rev. Lett. 90, 120404 (2003)], being completed by Gleason's theorem. This provides also a method for derivation of the Born rule.