Multiplayer XOR games and quantum communication complexity with clique-wise entanglement
Jop Briet, Harry Buhrman, Troy Lee, Thomas Vidick

TL;DR
This paper explores the limits of quantum entanglement in multiplayer XOR games, extending mathematical inequalities to bound quantum advantages and applying these results to quantum communication complexity.
Contribution
It generalizes Grothendieck's inequality to multiplayer XOR games with complex entanglement, solving open problems in operator algebras and quantum communication complexity.
Findings
Quantum entanglement provides at most a constant advantage in XOR games.
The discrepancy method remains a valid lower bound in quantum communication models.
Extended inequalities bound the quantum-classical gap in multiplayer settings.
Abstract
XOR games are a simple computational model with connections to many areas of complexity theory. Perhaps the earliest use of XOR games was in the study of quantum correlations. XOR games also have an interesting connection to Grothendieck's inequality, a fundamental theorem of analysis, which shows that two players sharing entanglement can achieve at most a constant factor advantage over players following classical strategies in an XOR game. Perez-Garcia et al. show that when the players share GHZ states, this advantage is bounded by a constant. We use a multilinear generalization of Grothendieck's inequality due to Blei and Tonge to simplify the proof of the second result and extend it to the case of so-called Schmidt states, answering an open problem of Perez-Garcia et al. Via a reduction given in that paper, this answers a 35-year-old problem in operator algebras due to Varopoulos,…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Quantum Computing Algorithms and Architecture · Cryptography and Data Security
