How Interference Effects in Mixtures Determine the Rules of Quantum Mechanics

TL;DR

This paper demonstrates that the indistinguishability properties of mixed quantum states align exclusively with standard quantum mechanics, ruling out several exotic alternative models through proposed experimental methods.

Contribution

It shows that the properties of mixed states support the Hilbert space framework and proposes experiments to eliminate exotic quantum models.

Findings

Elementary indistinguishability properties are consistent only with standard quantum mechanics.

Exotic models like quaternionic and octonionic variants can be experimentally ruled out.

Results hold even in low-dimensional systems.

Abstract

It is shown that elementary indistinguishability properties of partially polarized mixtures are consistent only with the conventional Hilbert space model of quantum mechanics and a few exotic alternatives. This applies even in low dimensions where quantum logic and Gleason's theorem give either weak or no constraints. Experimental methods for eliminating the exotic cases (which include quaternionic and octonionic variants of quantum mechanics) are described.