Density operators and selective measurements

TL;DR

This paper proposes a framework for describing selective quantum measurements using non-normalized density operators, challenging the common assumption that such operators must be normalized for statistical interpretation.

Contribution

It introduces a non-normalized density operator approach inspired by Schwinger's algebra, expanding the theoretical understanding of quantum measurement representations.

Findings

Density operators used are not normalized.

The approach is inspired by Schwinger's algebra.

Applications requiring normalized density operators are not identified.

Abstract

It is widely believed that statistical interpretation of quantum mechanics requires that density operators representing quantum states be normalized. We present a description of selective measurements in terms of density operators. The description is inspired by Schwinger's Algebra of Microscopic Measurements. Density operators used are not normalized. We do not know applications of density operators requiring normalization.