Quantum selective measurement as a quasilinear evolution

TL;DR

This paper introduces a continuous nonlinear evolution as an alternative to instantaneous state reduction in quantum measurement, maintaining key properties like no-signaling and ensemble equivalence.

Contribution

It proposes a novel nonlinear evolution model for quantum measurement that preserves ensemble equivalence and key measurement features.

Findings

Final states match von Neumann projection outcomes

Evolution preserves no-signaling principle

Converges to eigenstates regardless of initial state

Abstract

We propose replacing the instantaneous state reduction in von Neumann selective measurement with continuous nonlinear evolution. Despite its nonlinearity, this evolution preserves the equivalence of quantum ensembles and hence obeys the no-signaling principle. Its final states coincide with those produced by the von Neumann projection. The defining features of rank-one projective measurement are retained: convergence to the eigenstate of the observable associated with the selected outcome, independence of this final state from the initial state, and consistent action on entangled states.