Bifurcation in Quantum Measurement

TL;DR

This paper introduces a generic, reversible quantum measurement model demonstrating how a large system induces a bifurcation process, leading to eigenstate collapse consistent with the Born rule.

Contribution

It presents a new model of quantum measurement within reversible mechanics, illustrating a bifurcation mechanism for state collapse in large systems.

Findings

Large system A causes initial states to bifurcate into two subsets.

Each subset leads the measured system to an eigenstate.

Probabilities align with the Born rule.

Abstract

We present a generic model of (non-destructive) quantum measurement. Being formulated within reversible quantum mechanics, the model illustrates a mechanism of a measurement process --- a transition of the measured system to an eigenstate of the measured observable. The model consists of a two-level system $\mu$ interacting with a larger system $A$, consisting of smaller subsystems. The interaction is modelled as a scattering process. Restricting the states of $A$ to product states leads to a bifurcation process: In the limit of a large system $A$, the initial states of $A$ that are efficient in leading to a final state are divided into two separated subsets. For each of these subsets, $\mu$ ends up in one of the eigenstates of the measured observable. The probabilities obtained in this branching confirm the Born rule.