What Happens in a Measurement?

TL;DR

This paper investigates the conditions under which a Lindblad equation models quantum measurements, showing that the late-time behavior aligns with the Born rule and is independent of specific operator details.

Contribution

It provides necessary and sufficient conditions for Lindblad equations to produce measurement-like outcomes with the correct probabilities.

Findings

Late-time density matrix converges to measurement states.

Probabilities match the Born rule.

Explicit solutions for Lindblad equations under these conditions.

Abstract

It is assumed that in a measurement the system under study interacts with a macroscopic measuring apparatus, in such a way that the density matrix of the measured system evolves according to the Lindblad equation. Under an assumption of non-decreasing von Neumann entropy, conditions on the operators appearing in this equation are given that are necessary and sufficient for the late-time limit of the density matrix to take the form appropriate for a measurement. Where these conditions are satisfied, the Lindblad equation can be solved explicitly. The probabilities appearing in the late-time limit of this general solution are found to agree with the Born rule, and are independent of the details of the operators in the Lindblad equation.