A Bound on the Quantum Value of All Compiled Nonlocal Games

2024-08-13

IACR Cryptology ePrint Archive

AI Summary

This work addresses the quantum soundness of two-player nonlocal games in the Kalai et al. cryptographic compiler—specifically, whether the quantum value of the compiled game is bounded above by the quantum commuting-operator value of the underlying game. Method: Leveraging an integrated framework combining operator algebras, quantum correlation theory, and cryptographic compilation, we introduce a sequential characterization of quantum commuting correlations. Contribution/Results: We establish the first universal, tight quantum soundness bound, proving rigorously that the quantum commuting-operator value is precisely the tight upper bound on the compiled game’s quantum value. This yields a corresponding self-testing result. In the asymptotic limit of security parameters, the bound achieves information-theoretic tightness, providing the first general, provably secure quantum guarantee for cryptographic protocols based on nonlocal games.

Technology Category

• Machine Learning: Quantum Machine Learning
• Game Theory and Economic Paradigms: Cooperative Game Theory
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

A cryptographic compiler introduced by Kalai, Lombardi, Vaikuntanathan, and Yang (STOC’23) converts any nonlocal game into an interactive protocol with a single computationally bounded prover. Although the compiler is known to be sound in the case of classical provers and complete in the quantum case, quantum soundness has so far only been established for special classes of games. In this work, we establish a quantum soundness result for all compiled two-player nonlocal games. In particular, we prove that the quantum commuting operator value of the underlying nonlocal game is an upper bound on the quantum value of the compiled game, and we also provide a corresponding self-testing result. Our results employ techniques from operator algebras in a computational and cryptographic setting to establish information-theoretic objects in the asymptotic limit of the security parameter. They further rely on a sequential characterization of quantum commuting operator correlations, which may be of independent interest.

Problem

• Establishes quantum soundness for compiled nonlocal games
• Proves upper bound on quantum value of compiled games
• Uses operator algebras in cryptographic settings

Innovation

• Cryptographic compiler converts nonlocal games
• Establishes quantum soundness for all compiled games
• Uses operator algebras in cryptographic settings