The POVM Theorem in Bohmian Mechanics

TL;DR

This paper explains the POVM theorem in Bohmian mechanics, which connects quantum measurements to statistical predictions based on particle positions.

Contribution

The paper systematically presents the POVM theorem and its assumptions, clarifying its conceptual foundations and scope in Bohmian mechanics.

Findings

The POVM theorem is grounded in the quantum equilibrium hypothesis and describes measurement outcomes via a positive operator-valued measure.

The paper clarifies the assumptions and conceptual foundations underlying the POVM theorem in Bohmian mechanics.

It discusses the limits and scope of what can be measured within the framework of Bohmian mechanics.

Abstract

The POVM theorem is a central result in Bohmian mechanics, grounding the measurement formalism of standard quantum mechanics in a statistical analysis based on the quantum equilibrium hypothesis (the Born rule for Bohmian particle positions). It states that the outcome statistics of an experiment are described by a positive operator-valued measure (POVM) acting on the Hilbert space of the measured system. In light of recent debates about the scope and status of this result, we provide a systematic presentation of the POVM theorem and its underlying assumptions with a focus on their conceptual foundations and physical justifications. We conclude with a brief discussion of the scope of the POVM theorem—especially the sense in which it does (and does not) place limits on what is “measurable” in Bohmian mechanics.