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

TL;DR

This paper explores the connection between Tsirelson's bound and Landauer's principle within a single-qubit game, revealing how reversibility and system nature influence optimal success probabilities and entropic costs.

Contribution

It demonstrates that Tsirelson's bound applies to a single-system game and links quantum bounds to thermodynamic costs through Landauer's principle.

Findings

Tsirelson's bound holds in the single-qubit game setting.

Optimal success depends on gate reversibility and system nature.

Entropic costs relate to the irreversibility of operations.

Abstract

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 analyse the bounds obtained in light of Landauer's principle, showing the entropic costs of the erasure associated with the game. This shows a connection between the reversibility in fundamental operations embodied by Landauer's principle and Tsirelson's bound, that arises from the restricted physics of a unitarily-evolving single-qubit system.