Advantage of Greenberger-Horne-Zeilinger correlation in communication complexity: A step beyond the conventional Greenberger-Horne-Zeilinger paradox
Phys. Rev. A 112, 012214 – Published 17 July, 2025
DOI: https://doi.org/10.1103/hwgb-g93f
Abstract
We propose a randomized variant of the Greenberger-Horne-Zeilinger (GHZ) game where promise conditions for input distributions are selected uniform randomly from different possibilities, and disclosed to a single party only. Despite this asymmetry, the game is deterministically winnable using the GHZ correlation that yields perfect success in the original GHZ pseudotelepathy game. The introduced randomization, however, reveals a higher operational advantage in a class of multipartite communication complexity tasks, where inputs are distributed among distant parties and a designated function must be computed by one of them. Classical strategies require two bits of communication to the computing node from each of the other parties, while preshared GHZ states enable the same task with only one bit per party. This separation demonstrates a superior utility of GHZ correlations in multipartite protocols and showcases an enhanced operational power of genuine entanglement in multipartite quantum communication complexity tasks.
