Year: 2026
Type: article
Abstract: Nonlocal games are a foundational tool for understanding entanglement and constructing quantum protocols in settings with multiple spatially separated quantum devices. In this work, we continue the study initiated by Kalai et al. (STOC '23) of compiled nonlocal games, played between a classical verifier and a single cryptographically limited quantum device. Our main result is that the compiler proposed by Kalai et al. is sound for any two-player XOR game. A celebrated theorem of Tsirelson shows that for XOR games, the quantum value is exactly given by a semidefinite program, and we obtain our result by showing that the SDP upper bound holds for the compiled game up to a negligible error arising from the compilation. This answers a question raised by Natarajan and Zhang (FOCS '23), who showed soundness for the specific case of the CHSH game. Using our techniques, we obtain several additional results, including (1) tight bounds on the compiled value of parallel-repeated XOR games, (2) operator self-testing statements for any compiled XOR game, and (3) a “nice'' sum-of-squares certificate for any XOR game, from which operator rigidity is manifest.
Source: Quantum
Authors: David Cui, Giulio Malavolta, Arthur Mehta, Anand Natarajan, Connor Paddock, Simon Schmidt, Michael Walter, Tina Zhang
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $215
Funders: Deutsche Forschungsgemeinschaft, Bundesministerium für Bildung und Forschung, Nederlandse Organisatie voor Wetenschappelijk Onderzoek, Simons Institute for the Theory of Computing, University of California Berkeley, Natural Sciences and Engineering Research Council of Canada, HORIZON EUROPE European Research Council
OpenAlex ID: W4392341514