A nonlocal game for witnessing quantum networks

Ming-Xing Luo

doi:10.1038/s41534-019-0203-6

Abstract

Nonlocal game as a witness of the nonlocality of entanglement is of fundamental importance in various fields. The well-known nonlocal games or equivalent linear Bell inequalities are only useful for Bell networks consisting of single entanglement. Our goal in this paper is to propose a unified method for constructing cooperating games in network scenarios. We propose an efficient method to construct multipartite nonlocal games from any graphs. The main idea is the graph representation of entanglement-based quantum networks. We further specify these graphic games with quantum advantages by providing a simple sufficient and necessary condition. The graphic games imply a linear Bell testing of the nonlocality of general quantum networks consisting of EPR states. It also allows generating new instances going beyond CHSH game. These results have interesting applications in quantum networks, Bell theory, computational complexity, and theoretical computer science.

Highlights

A nonlocal game is generally described as multiple spaceseparated players interacting with a referee
A nonlocal game allows all the players to determine a joint strategy from the complete knowledge of inputs distribution and the predicate conditions for win
One fundamental problem is to determine whether quantum mechanics is superior to classical theory in terms of nonlocal tasks

Summary

INTRODUCTION

A nonlocal game is generally described as multiple spaceseparated players interacting with a referee. The corresponding procedure can be featured by a generalized hidden variable model with classical sources or quantum sources.[1] One fundamental problem is to determine whether quantum mechanics is superior to classical theory in terms of nonlocal tasks These evaluations are equivalent to solving special optimization problems from Tsirelson’s reductions.[7] no efficient algorithm exists for general multipartite nonlocal games.[8,9,10,11,12,13]. The graphic game extends the guessing your neighbor’s input (GYNI) game.[50,51] The present model provides novel instances to feature nonlocal games with different performances.[52]

RESULT

DISCUSSION