Contextuality of Approximate Measurements

TL;DR

This paper critiques the MKC claim that finite measurement precision nullifies the Kochen-Specker theorem, showing that contextuality re-emerges when considering approximate joint measurements of non-commuting observables.

Contribution

It extends the analysis of MKC models by investigating approximate joint measurements, demonstrating that contextuality persists beyond strict measurement assumptions.

Findings

Nullification of Kochen-Specker theorem is incomplete under approximate measurements.

Contextuality re-emerges when considering non-commuting observables.

MKC models do not fully eliminate quantum contextuality.

Abstract

The claim of Meyer, Kent and Clifton (MKC) that finite precision measurement nullifies the Kochen-Specker theorem is criticised. It is argued that, although MKC have nullified the Kochen-Specker theorem strictly so-called, there are other, related propositions which are not nullified. The argument given is an elaboration of some of Mermin's critical remarks. Although MKC allow for the fact that the observables to be measured cannot be precisely specified, they continue to assume that the observables which are actually measured are strictly commuting. As Mermin points out, this assumption is unjustified. Consequently, the analysis of MKC is incomplete. To make it complete one needs to investigate the predictions their models make regarding approximate joint measurements of non-commuting observables. Such an investigation is carried out, using methods previously developed in connection with approximate joint measurements of position and momentum. It is shown that a form of contextuality then re-emerges.