Complete Characterization of Pure Quantum Measurements and Quantum Channels

TL;DR

This paper provides a comprehensive characterization of pure quantum measurements and channels, identifying conditions under which measurements are free from classical and quantum noise across various quantum systems.

Contribution

It offers a complete characterization of pure quantum measurements and channels, including conditions for sharp measurements to be noise-free, applicable to discrete, continuous, and infinite-dimensional systems.

Findings

Pure measurements are extremals in the convex set of POVMs.

Sharp measurements are inherently noise-free and cannot be irreversibly transformed into other POVMs.

Approximate noise-freeness may also hold for pure measurements.

Abstract

We give a complete characterization for pure quantum measurements, i.e., for POVMs which are extremals in the convex set of all POVMs. Such measurements are free from classical noise. The characterization is valid both in discrete and continuous cases, and also in the case of an infinite Hilbert space. We show that sharp measurements are clean, i.e. they cannot be irreversibly connected to another POVMs via quantum channels and thus they are free from any additional quantum noise. We exhibit an example which demonstrates that this result could also be approximately true for pure measurements.