Entropic Version of the Greenberger-Horne-Zeilinger Paradox

TL;DR

This paper presents an entropic reformulation of the GHZ paradox, demonstrating that quantum systems can defy classical predictions by allowing complete knowledge of some properties while remaining completely uncertain about others.

Contribution

It introduces an information-theoretic version of the GHZ paradox, highlighting quantum-classical discrepancies in knowledge about system properties.

Findings

Quantum states can violate classical predictions of property relations.

Quantum theory allows full knowledge of certain properties while remaining completely uncertain about others.

The entropic formulation clarifies the nature of quantum nonlocality and contextuality.

Abstract

Consider four binary +-1 variables A, B, C and D for which classical reasoning implies ABCD = 1. In this case the knowledge of A, B, C automatically provides knowledge of D because D = ABC. However, the Greenberger-Horne-Zeilinger paradox shows that despite classical prediction one can find quantum states and observables with well defined outcomes for which D = -ABC. In this work we formulate an information-theoretic version of this paradox. We show that for a tripartite quantum system one can find a set of four properties for which classical reasoning implies that D = ABC, yet quantum theory predicts that one can know everything about A, B, C and nothing about D.