Quantum bounds on multiplayer linear games and device-independent witness 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.

7+8 pages

References in corpus (7)

• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Measure of genuine multipartite entanglement with computable lower bounds
• Efficient Toffoli Gates Using Qudits
• The structure of multidimensional entanglement in multipartite systems
• Witnessing genuine multipartite entanglement with positive maps
• Multi-setting Bell inequality for qudits
• Characterising the Performance of XOR Games and the Shannon Capacity of Graphs

Cited by in corpus (7)

• Semi-device-independent characterisation of multipartite entangled states and measurements
• Device Independent Quantum Secret Sharing in Arbitrary Even Dimension
• Generalized XOR games with $d$ outcomes and the task of non-local computation
• Trade-offs in multi-party Bell inequality violations in qubit networks
• Analytic Semi-device-independent Entanglement Quantification for Bipartite Quantum States
• Quantifying Multipartite Quantum Entanglement in a Semi-Device-Independent Manner
• Constructive nonlocal games with very small classical values