A universal property for sequential measurement

TL;DR

This paper characterizes the sequential measurement operation in quantum mechanics using axioms, providing a universal property for the sequential product in von Neumann algebras.

Contribution

It introduces four axioms that uniquely determine the sequential product, offering a foundational understanding of sequential measurements.

Findings

Four axioms fully characterize the sequential product.

The sequential product is uniquely determined by these axioms.

Provides a universal property for sequential measurement in quantum theory.

Abstract

We study the sequential product, the operation $p * q = \sqrt{p} q \sqrt{p}$ on the set of effects of a von Neumann algebra that represents sequential measurement of first $p$ and then $q$. We give four axioms which completely determine the sequential product.