Quantum bounds on multiplayer linear games and device-independent witness of genuine tripartite entanglement

TL;DR

This paper extends bounds on quantum values from two-player to multi-player linear games, demonstrating limitations on certain nonlocal boxes and providing a method for device-independent detection of genuine tripartite entanglement.

Contribution

It generalizes a bound on quantum game values to n-player linear games and introduces a systematic approach for device-independent entanglement witnessing.

Findings

Bound the quantum value of multi-player linear games using game matrix norms.

Show that certain nontrivial functional boxes cannot be realized quantum mechanically.

Develop a method for device-independent detection of genuine tripartite entanglement.

Abstract

Here we study multiplayer linear games, a natural generalization of XOR games to multiple outcomes. We generalize a recently proposed efficiently computable bound, in terms of the norm of a game matrix, on the quantum value of 2-player games to linear games with $n$ players. As an example, we bound the quantum value of a generalization of the well-known CHSH game to $n$ players and $d$ outcomes. We also apply the bound to show in a simple manner that any nontrivial functional box, that could lead to trivialization of communication complexity in a multiparty scenario, cannot be realized in quantum mechanics. We then present a systematic method to derive device-independent witnesses of genuine tripartite entanglement.