# 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.

## Key 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.