Distinguishing quantum measurements of observables in terms of state transformers

TL;DR

This paper introduces a framework for quantum measurements using state transformers, providing algebraic and geometric characterizations of measurement types like repeatable and ideal measurements.

Contribution

It develops a unified framework relating Kraus representations to measurement types and characterizes measurement classes through algebraic and geometric conditions.

Findings

Defines state transformers in quantum measurement.

Characterizes measurement types algebraically and geometrically.

Provides conditions distinguishing measurement classes.

Abstract

The modern framework of state transformers, i. e., the first Kraus representation of quantum measurement, is introduced and related both to the known textbook concepts and to measurement-interaction evolution (the second Kraus representation). In this framework the known kinds of measurements of ordinary (as distinct from generalized) observables are distinguished by necessary and sufficient conditions. Thus, repeatable,nonrepeatable, and ideal measurements are characterized both algebraically and geometrically in terms of polar factors of state transformers.