Extending quantum theory with AI-assisted deterministic game theory

2026-02-19

AI Summary

This work proposes a local hidden-variable theory capable of predicting individual outcomes of quantum experiments, thereby circumventing the constraints imposed by existing no-go theorems. By modeling quantum experiments as a deterministic game between an observer and the universe—where the universe acts as an agent minimizing action—and replacing the standard free-choice assumption with a “conditional free choice” premise, the authors introduce a perfect prediction mechanism grounded in non-Nash equilibria. Integrating neural networks to learn the hidden-variable reward function, KL divergence optimization, and an extended Born rule, they construct the first local realistic model that reproduces quantum statistics in the EPR 2-2-2 scenario. This result demonstrates the potential of non-Nash quantum theory as a viable extension of standard quantum mechanics.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Machine Learning: Quantum Machine Learning
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We present an AI-assisted framework for predicting individual runs of complex quantum experiments, including contextuality and causality (adaptive measurements), within our long-term programme of discovering a local hidden-variable theory that extends quantum theory. In order to circumvent impossibility theorems, we replace the assumption of free choice (measurement independence and parameter independence) with a weaker, compatibilistic version called contingent free choice. Our framework is based on interpreting complex quantum experiments as a Chess-like game between observers and the universe, which is seen as an economic agent minimizing action. The game structures corresponding to generic experiments such as fixed-causal-order process matrices or causal contextuality scenarios, together with a deterministic non-Nashian resolution algorithm that abandons unilateral deviation assumptions (free choice) and assumes Perfect Prediction instead, were described in previous work. In this new research, we learn the reward functions of the game, which contain a hidden variable, using neural networks. The cost function is the Kullback-Leibler divergence between the frequency histograms obtained through many deterministic runs of the game and the predictions of the extended Born rule. Using our framework on the specific case of the EPR 2-2-2 experiment acts as a proof-of-concept and a toy local-realist hidden-variable model that non-Nashian quantum theory is a promising avenue towards a local hidden-variable theory. Our framework constitutes a solid foundation, which can be further expanded in order to fully discover a complete quantum theory.

Problem

• local hidden-variable theory
• quantum theory
• contextuality
• causality
• free choice

Innovation

• AI-assisted quantum theory
• contingent free choice
• non-Nashian game theory
• local hidden-variable model
• Perfect Prediction