Stronger Nonlocality in GHZ States: A Step Beyond the Conventional GHZ Paradox

TL;DR

This paper introduces a randomized GHZ game variant that reveals a stronger form of quantum nonlocality, demonstrating enhanced nonlocal correlations with greater communication advantages than traditional GHZ paradoxes.

Contribution

The authors develop a randomized GHZ game with a novel promise condition, showing it exhibits stronger nonlocality and operational advantages over conventional GHZ paradoxes.

Findings

Randomized GHZ game can be perfectly resolved with GHZ states.

Stronger nonlocality demonstrated through increased communication complexity.

Operational implications for quantum communication protocols.

Abstract

The Greenberger-Horne-Zeilinger (GHZ) paradox, involving quantum systems with three or more subsystems, offers an 'all-vs-nothing' test of quantum nonlocality. Unlike Bell tests for bipartite systems, which reveal statistical contradictions, the GHZ paradox demonstrates a definitive (i.e. 100%) conflict between local hidden variable theories and quantum mechanics. Given this, how can the claim made in the title be justified? The key lies in recognising that GHZ games are typically played under a predefined promise condition for input distribution. By altering this promise, different GHZ games can be constructed. Here, we introduce a randomized variant of GHZ game, where the promise condition is randomly selected from multiple possibilities and revealed to only one of the parties chosen randomly. We demonstrate that this randomized GHZ paradox can also be perfectly resolved using a GHZ state, revealing a potentially stronger form of nonlocality than the original paradox. The claim of enhanced nonlocality is supported by its operational implications: correlations yielding perfect success in the randomized game offer a greater communication advantage than traditional GHZ correlations in a distributed multi-party communication complexity task.