Solving the Greenberger-Horne-Zeilinger paradox: an explicitly local and realistic model of hidden variables for the GHZ quantum state

TL;DR

This paper identifies an overlooked assumption in the GHZ paradox related to an absolute angular reference frame, and constructs a local, realistic hidden-variable model that reproduces quantum predictions without this assumption.

Contribution

It reveals the implicit assumption of an absolute reference frame in the GHZ argument and develops a local, realistic hidden-variable model that aligns with quantum mechanics.

Findings

The GHZ paradox relies on an unphysical absolute reference frame assumption.

A local and realistic hidden-variable model for the GHZ state is constructed.

The model reproduces quantum predictions without violating locality or realism.

Abstract

The Greenberger-Horne-Zeilinger~(GHZ) version of the Einstein-Podolsky-Rosen~(EPR) paradox is widely regarded as a conclusive logical argument that rules out the possibility of describing quantum phenomena within the framework of a local and realistic model of hidden variables in which the observers are free to choose their own experimental settings. In this paper we show, however, that the GHZ argument implicitly relies on an additional crucial assumption, which is not required by fundamental physical principles and had gone unnoticed. Namely, we note that the argument implicitly assumes the existence of an absolute angular frame of reference with respect to which the polarization properties of the hypothetical hidden configurations of the entangled particles as well as the orientation of the measurement apparatus that test the system can be defined. We further note that such an absolute frame of reference would not exist if the hidden configurations of the entangled particles spontaneously break the gauge rotational symmetry. Indeed, by skipping this unnecessary additional assumption we are able to build an explicitly local and realistic model of hidden variables for the GHZ state, which complies with the 'free-will' hypothesis and reproduces the quantum mechanical predictions, and thus completes the description of the system in the EPR sense.