Sequential measurements of conjugate observables

TL;DR

This paper develops a unified mathematical framework for sequential measurements of conjugate quantum observables, demonstrating that any covariant observable can be realized through such sequential measurements in finite and infinite-dimensional systems.

Contribution

It provides a structure theorem for covariant instruments and shows the universality of sequential measurements for all Weyl-Heisenberg covariant observables.

Findings

All covariant observables can be implemented as sequential measurements.

The framework applies to both finite and infinite-dimensional systems.

Includes sequential spin and position-momentum measurements.

Abstract

We present a unified treatment of sequential measurements of two conjugate observables. Our approach is to derive a mathematical structure theorem for all the relevant covariant instruments. As a consequence of this result, we show that every Weyl-Heisenberg covariant observable can be implemented as a sequential measurement of two conjugate observables. This method is applicable both in finite and infinite dimensional Hilbert spaces, therefore covering sequential spin component measurements as well as position-momentum sequential measurements.