Overview of projective quantum measurements

TL;DR

This paper reviews the theory of projective quantum measurements, emphasizing the Stinespring representation's role in connecting quantum measurement theory with experimental practice and providing conceptual insights.

Contribution

It elucidates the Stinespring unitary representation of measurements, linking it with Kraus and von Neumann forms, and highlights its significance in understanding measurement processes and locality.

Findings

Stinespring representation guarantees by quantum axioms

Connects theory with experimental measurement protocols

Ensures compatibility of quantum operations with relativity

Abstract

We provide an overview of standard "projective" quantum measurements with the goal of elucidating connections between theory and experiment. We make use of a unitary "Stinespring" representation of measurements on a dilated Hilbert space that includes both the physical degrees of freedom and those of the measurement apparatus. We explain how this unitary representation (i) is guaranteed by the axioms of quantum mechanics, (ii) relates to both the Kraus and von Neumann representations, and (iii) corresponds to the physical time evolution of the system and apparatus during the measurement process. The Stinespring representation also offers significant conceptual insight into measurements, helps connects theory and experiment, is particularly useful in describing protocols involving midcircuit measurements and outcome-dependent operations, and establishes that all quantum operations are compatible with relativistic locality, among other insights.