Quantum discord and noncontextual hidden variables models

TL;DR

This paper investigates the limitations of noncontextual hidden variables models in quantum mechanics, showing they cannot reliably define quantum discord in two-dimensional systems due to non-uniqueness issues.

Contribution

It demonstrates the conflicts in dispersion free representations in hidden variables models and discusses the challenges in defining quantum discord within these models.

Findings

Noncontextual hidden variables models in d=2 lead to conflicting dispersion free expressions.

No unique criterion for quantum discord can be formulated in d=2 hidden variables space.

Speculative discussion on many-worlds interpretation of hidden variables models.

Abstract

It is shown that theoretically viable noncontextual hidden variables models in $d=2$ lead to conflicting dispersion free expressions in the analysis of the conditional measurement of two non-orthogonal projectors. No satisfactory criterion of the quantum discord, which relies on the analysis of conditional measurement, is formulated in the $d=2$ hidden variables space due to a lack of uniqueness of the dispersion free representation. We also make a speculative comment on a "many-worlds interpretation" of hidden variables models to account for the conditional measurement.