How to Measure the Quantum Measure

TL;DR

This paper proposes an experimental method to measure quantum measures in histories-based quantum theory using ancillas and unitary transformations, enabling verification of microscopic events with minimal disturbance.

Contribution

It introduces a practical scheme to determine quantum measures experimentally, bridging the gap between theoretical measures and observable outcomes in quantum history frameworks.

Findings

Method to couple ancillas and perform unitary transformations to measure $ulE$

Relates measurement outcomes to quantum measure $ulE$ with known proportionality

Discusses minimally disturbing verification of microscopic events

Abstract

The histories-based framework of Quantum Measure Theory assigns a generalized probability or measure $\mu(E)$ to every (suitably regular) set $E$ of histories. Even though $\mu(E)$ cannot in general be interpreted as the expectation value of a selfadjoint operator (or POVM), we describe an arrangement which makes it possible to determine $\mu(E)$ experimentally for any desired $E$. Taking, for simplicity, the system in question to be a particle passing through a series of Stern-Gerlach devices or beam-splitters, we show how to couple a set of ancillas to it, and then to perform on them a suitable unitary transformation followed by a final measurement, such that the probability of a final outcome of "yes" is related to $\mu(E)$ by a known factor of proportionality. Finally, we discuss in what sense a positive outcome of the final measurement should count as a minimally disturbing verification that the microscopic event $E$ actually happened.