Two-player entangled games are NP-hard

TL;DR

This paper proves that approximating the maximum success probability in certain two-player quantum entangled games is NP-hard, leading to a significant simplification of the complexity class inclusion involving two entangled provers.

Contribution

It establishes NP-hardness for two-player entangled games and simplifies the proof of the NEXP inclusion in MIP* with only two provers, improving previous results.

Findings

NP-hardness of approximating success probability in two-player entangled games

Simplified proof of NEXP ⊆ MIP* with two provers

Improved analysis of low-degree test against entangled provers

Abstract

We show that the maximum success probability of players sharing quantum entanglement in a two-player game with classical questions of logarithmic length and classical answers of constant length is NP-hard to approximate to within constant factors. As a corollary, the inclusion $\mathrm{NEXP}\subseteq\mathrm{MIP}^*$, first shown in [IV12] with three provers, holds with two provers only. The proof is based on a simpler, improved analysis of the low-degree test Raz and Safra (STOC'97) against two entangled provers.