A non-Hermitian loop for a quantum measurement

TL;DR

This paper introduces a non-Hermitian framework for quantum measurement, proposing that state collapse occurs when the Hamiltonian completes a parameter loop, and demonstrates chiral state conversion in two-level systems to eliminate superpositions.

Contribution

It presents a novel non-Hermitian approach to model quantum measurement and introduces chiral state conversion as a mechanism to effectively eliminate superpositions.

Findings

Collapse occurs when Hamiltonian completes a parameter loop

Chiral state conversion enables superposition elimination

Framework allows simulation of quantum measurements in classical systems

Abstract

Here we present a non-Hermitian framework for modeling state-vector collapse under unified dynamics described by Schr\"odinger's equation. Under the premise of non-Hermitian Hamiltonian dynamics, we argue that collapse has to occur when the Hamiltonian completes a closed loop in the parameter space encoding the interaction with the meter. For two-level systems, we put forward the phenomenon of chiral state conversion as a mechanism for effectively eliminating superpositions. This perspective opens a way to simulate quantum measurements in classical systems that up to now were restricted to the Schr\"odinger part of the quantum dynamics.