# What Quantum Measurements Measure

## TL;DR

This paper addresses the second measurement problem in quantum mechanics, demonstrating how measurement outcomes relate to prior properties using consistent histories, and clarifies the noncontextuality of quantum measurements.

## Contribution

It provides a solution to the second measurement problem for projective and POVM measurements, supporting that well-designed equipment reveals intended properties and clarifies measurement contextuality.

## Key findings

- Measurements reveal properties they are designed to measure
- Quantum measurements are noncontextual in the original Bell-Mermin sense
- Application to EPR and Wheeler paradoxes offers new insights

## Abstract

A solution to the second measurement problem, determining what prior microscopic properties can be inferred from measurement outcomes ("pointer positions"), is worked out for projective and generalized (POVM) measurements, using consistent histories. The result supports the idea that equipment properly designed and calibrated reveals the properties it was designed to measure. Applications include Einstein's hemisphere and Wheeler's delayed choice paradoxes, and a method for analyzing weak measurements without recourse to weak values. Quantum measurements are noncontextual in the original sense employed by Bell and Mermin: if $[A,B]=[A,C]=0,\, [B,C]\neq 0$, the outcome of an $A$ measurement does not depend on whether it is measured with $B$ or with $C$. An application to Bohm's model of the Einstein-Podolsky-Rosen situation suggests that a faulty understanding of quantum measurements is at the root of this paradox.