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

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 nonzero discord. Classical behavioral strategies, constrained by memory loss, cannot achieve this coordination. When reinterpreted as a two-player game, the same construction yields a Nash equilibrium in behavioral quantum strategies. This result offers a quantum analogue of Kuhn’s Theorem: quantum discord substitutes for strategic memory, enabling coordination in settings where classical agents fail. These findings highlight discord as a minimal yet sufficient quantum resource for restoring equilibrium behavior under imperfect recall.