Objectivity in quantum measurement

TL;DR

This paper demonstrates that objectivity in quantum measurements requires orthogonal measurement bases, explaining why classical measurement bases are orthogonal and highlighting the role of macroscopicality in classicality.

Contribution

It establishes a fundamental link between objectivity in measurement and the orthogonality of measurement bases in quantum mechanics.

Findings

Objectivity constrains quantum measurement bases to be orthogonal.

Orthogonality of measurement bases explains classical measurement axioms.

Macroscopicality supports the emergence of classicality from quantum measurements.

Abstract

The objectivity is a basic requirement for the measurements in the classical world, namely, different observers must reach a consensus on their measurement results, so that they believe that the object exists "objectively" since whoever measures it obtains the same result. We find that this simple requirement of objectivity indeed imposes an important constraint upon quantum measurements, i.e., if two or more observers could reach a consensus on their quantum measurement results, their measurement basis must be orthogonal vector sets. This naturally explains why quantum measurements are based on orthogonal vector basis, which is proposed as one of the axioms in textbooks of quantum mechanics. The role of the macroscopicality of the observers in an objective measurement is discussed, which supports the belief that macroscopicality is a characteristic of classicality.