A Review of Unitary Quantum Premeasurement Theory An Algebraic Study of Basic Kinds of Premeasurements

TL;DR

This paper provides a comprehensive algebraic review of quantum premeasurement theory, focusing on unitary dynamics, definitions, classifications, and connections with existing research, without involving collapse or environment effects.

Contribution

It offers a unified, logical derivation of various types of quantum premeasurements within the standard formalism, including ideal, nondemolition, and disentangled premeasurements.

Findings

Defined general exact premeasurement in 7 ways

Characterized nondemolition premeasurement in 10 ways

Classified all premeasurements using disentangled and entangled frameworks

Abstract

A detailed theory of quantum premeasurement dynamics is presented in which a unitary composite-system operator that contains the relevant object-measuring-instrument interaction brings about the final premeasurement state. It does not include collapse, and it does not consider the environment. It is assumed that a discrete degenerate or non-degenerate observable is measured. Premeasurement is defined by the calibration condition, which requires that every initially statistically sharp value of the measured observable has to be detected with statistical certainty by the measuring instrument. The entire theory is derived as a logical consequence of this definition using the standard quantum formalism. The study has a comprehensive coverage, hence the article is actually a topical review. Connection is made with results of other authors, particularly with basic works on premeasurement. The article is a conceptual review, not a historical one. General exact premeasurement is defined in 7 equivalent ways. Nondemolition premeasurement, defined by requiring preservation of any sharp value of the measured observable, is characterized in 10 equivalent ways. Overmeasurement, i. e., a process in which the observable is measured on account of being a function of a finer observable that is actually measured, is discussed. Disentangled premeasurement, in which, by definition, to each result corresponds only one pointer-observable state in the final composite-system state, is investigated. Ideal premeasurement, a special case of both nondemolition premeasurement and disentangled premeasurement, is defined, and its most important properties are discussed. Finally, disentangled and entangled premeasurements, in conjunction with nondemolition or demolition premeasurements, are used for classification of all premeasurements.