When Recall Fails, Discord Remembers: A Quantum Analogue of Kuhn's Theorem

TL;DR

This paper demonstrates that quantum discord allows behavioral strategies in imperfect recall games to replicate classical mixed strategies, effectively substituting for strategic memory and enhancing coordination beyond classical capabilities.

Contribution

It introduces a quantum analogue of Kuhn's theorem showing discord's role in enabling classical-like strategic coordination without entanglement.

Findings

Quantum discord enables classical strategy replication.

Imperfect recall strategies benefit from quantum resources.

Quantum discord acts as a minimal resource for strategic enhancement.

Abstract

A behavioral quantum strategy is shown to replicate the payoff of a classical mixed strategy in an extensive-form game with imperfect recall, using only local measurements on a separable quantum state with zero entanglement and nonzero discord. Classical behavioral strategies, constrained by imperfect recall, cannot achieve this coordination. The result suggests a quantum analogue to Kuhn's classical equivalence: discord enables behavioral-style strategies to functionally substitute for strategic memory and recover coordination lost in the classical setting. This highlights quantum discord as a minimal and robust resource for extending bounded rationality beyond classical limits.