Quantitative quantum soundness for all multipartite compiled nonlocal games

2025-09-29

AI Summary

Existing KLVY compilers for multiparty nonlocal games only achieve quantitative quantum soundness in the bipartite setting; for general multiparty games, only asymptotic guarantees are known—leaving a critical theoretical gap. Method: We establish the first quantitative quantum reliability guarantee for the KLVY compiler against arbitrary multiparty nonlocal games by (i) leveraging quantum homomorphic encryption to reduce multiprover Bell tests to single-device interactive protocols; (ii) introducing an NPA-style hierarchy of quantum instruments and proving its completeness; and (iii) developing a geometric decomposition technique to isolate signaling and nonsignaling components in sequential strategies. Results: Integrating operational nonsignaling modeling, multiparty nonlocality analysis, and complexity-theoretic tools, we rigorously bound the power of malicious quantum provers. Our framework provides the first universal, quantitatively secure foundation for single-device quantum verification.

Technology Category

• Machine Learning: Quantum Machine Learning
• Game Theory and Economic Paradigms: Mechanism Design
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data

Abstract

Compiled nonlocal games transfer the power of Bell-type multi-prover tests into a single-device setting by replacing spatial separation with cryptography. Concretely, the KLVY compiler (STOC'23) maps any multi-prover game to an interactive single-prover protocol, using quantum homomorphic encryption. A crucial security property of such compilers is quantum soundness, which ensures that a dishonest quantum prover cannot exceed the original game's quantum value. For practical cryptographic implementations, this soundness must be quantitative, providing concrete bounds, rather than merely asymptotic. While quantitative quantum soundness has been established for the KLVY compiler in the bipartite case, it has only been shown asymptotically for multipartite games. This is a significant gap, as multipartite nonlocality exhibits phenomena with no bipartite analogue, and the difficulty of enforcing space-like separation makes single-device compilation especially compelling. This work closes this gap by showing the quantitative quantum soundness of the KLVY compiler for all multipartite nonlocal games. On the way, we introduce an NPA-like hierarchy for quantum instruments and prove its completeness, thereby characterizing correlations from operationally-non-signaling sequential strategies. We further develop novel geometric arguments for the decomposition of sequential strategies into their signaling and non-signaling parts, which might be of independent interest.

Problem

• Establishes quantitative quantum soundness for multipartite compiled nonlocal games
• Extends KLVY compiler security from bipartite to multipartite nonlocality scenarios
• Develops novel hierarchy and geometric methods for sequential strategy analysis

Innovation

• Quantitative quantum soundness for multipartite compiled games
• NPA-like hierarchy for quantum instruments characterization
• Geometric decomposition of sequential signaling strategies