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We introduce a simple single-system game inspired by theClauser-Horne-Shimony-Holt (CHSH) game. For qubit systems subjected to unitarygates and projective measurements, we prove that any strategy in our game canbe mapped to a strategy in the CHSH game, which implies that Tsirelson's boundalso holds in our setting. More generally, we show that the optimal successprobability depends on the reversible or irreversible character of the gates,the quantum or classical nature of the system and the system dimension. Weanalyse the bounds obtained in light of Landauer's principle, showing theentropic costs of the erasure associated with the game. This shows a connectionbetween the reversibility in fundamental operations embodied by Landauer'sprinciple and Tsirelson's bound, that arises from the restricted physics of aunitarily-evolving single-qubit system.

Tsirelson's bound and Landauer's principle in a single-system game