Quantum non-locality co-exists with locality

TL;DR

This paper demonstrates a form of quantum non-locality that coexists with locality by using imprecise joint probabilities, showing non-factorization even in uncorrelated states, thus reconciling non-locality with local descriptions.

Contribution

It introduces a novel perspective on quantum non-locality through imprecise joint probabilities, avoiding hidden variables and collapse, and showing non-local effects within standard quantum mechanics.

Findings

Imprecise joint probabilities reveal non-local effects without hidden variables.

Non-factorization occurs in uncorrelated states, indicating inherent non-locality.

Less precise probabilities restore factorization, linking non-locality to measurement precision.

Abstract

Quantum non-locality is normally defined via violations of Bell's inequalities that exclude certain classical hidden variable theories from explaining quantum correlations. Another definition of non-locality refers to the wave-function collapse thereby one can prepare a quantum state from arbitrary far away. In both cases one can debate on whether non-locality is a real physical phenomenon, e.g. one can employ formulations of quantum mechanics that does not use collapse, or one can simply refrain from explaining quantum correlations via classical hidden variables. Here we point out that there is a non-local effect within quantum mechanics, i.e. without involving hidden variables or collapse. This effect is seen via imprecise (i.e. interval-valued) joint probability of two observables, which replaces the ill-defined notion of the precise joint probability for non-commuting observables. It is consistent with all requirements for the joint probability, e.g. those for commuting observales. The non-locality amounts to a fact that (in a two-particle system) the joint imprecise probability of non-commuting two-particle observables (i.e. tensor product of single-particle observables) does not factorize into single-particle contributions, even for uncorrelated states of the two-particle system. The factorization is recovered for a less precise (i.e. the one involving a wider interval) joint probability. This approach to non-locality reconciles it with locality, since the latter emerges as a less precise description.