Incompleteness of measurement apparatuses

TL;DR

This paper demonstrates that quantum measurement apparatuses must be inherently incomplete to avoid noise, and introduces a refined concept of separation status crucial for understanding measurement in quantum mechanics.

Contribution

It shows that all measurement apparatuses are necessarily incomplete and proposes a new, improved definition of separation status in quantum measurement theory.

Findings

Apparatuses must be incomplete to function properly in quantum mechanics.

Quantum observables are represented by many incomplete measurement devices.

A new definition of separation status improves understanding of system preparation.

Abstract

A complete apparatus is defined as reacting to every state of the measured system. Standard quantum mechanics of indistinguishable particles is shown to imply that apparatuses must be incomplete or else they would be drowned out by noise. Each quantum observable is then an abstract representation of many measurement apparatuses, each incomplete in a different way. Moreover, a measured system must be prepared in a state that is orthogonal to the states of all particles of the same type in the environment. This is the main purpose of preparations. A system so prepared is said to have a "separation status". A new, more satisfactory definition of separation status than the spatial one proposed in previous papers then results. Conditions are specified under which the particles in the environment may be ignored as is usually done in the theory of measurement.