Irreversibility and non-classicality in a single-system game

Luciana Henaut (UCL), Lorenzo Catani (Chapman University), Dan Browne (UCL), Shane Mansfield (LIP6, Sorbonne Université), Anna Pappa (FU Berlin)

We introduce a simple single-system game inspired by the Clauser-Horne-Shimony-Holt (CHSH) game. For qubit systems subjected to unitary gates and projective measurements, we prove that any strategy in our game can be mapped to a strategy in the CHSH game, which implies that Tsirelson’s bound also holds in our setting. More generally, we show that the optimal success probability depends on the reversible or irreversible character of the gates, the quantum or classical nature of the system, and the system dimension. 

We focus on irreversibility and the use of quantum mechanics as the sources of computational advantages for the game. We analyze the former in light of Landauer’s principle, showing the entropic costs of the erasure associated with the game. 

On the other hand, quantum advantages can be explained by appealing to the presence of contextuality. We compare the two analysis and explore a possible connection between the erasure of information and contextuality.