Quantum collapse rules from the maximum relative entropy principle

TL;DR

This paper demonstrates that quantum collapse rules can be derived from an information-theoretic principle, specifically the maximum quantum relative entropy, providing a new foundational perspective on quantum measurement.

Contribution

It introduces a novel derivation of quantum collapse rules based on the maximum relative entropy principle, linking measurement to information theory.

Findings

Quantum collapse rules correspond to states maximizing quantum relative entropy.

Collapse rules are uniquely determined by information-theoretic constraints.

Provides an information-theoretic foundation for quantum measurement processes.

Abstract

We show that the von Neumann--Lueders collapse rules in quantum mechanics always select the unique state that maximises the quantum relative entropy with respect to the premeasurement state, subject to the constraint that the postmeasurement state has to be compatible with the knowledge gained in the measurement. This way we provide an information theoretic characterisation of quantum collapse rules by means of the maximum relative entropy principle.