Dimensionality Distinguishers
This work addresses the problem of distinguishing quantum dimensions for researchers in quantum information, though it appears incremental as it builds on the established CHSH game model.
The authors generalized the CHSH game to include all non-constant Boolean functions and measurement bases, constructing equivalence classes that enable dimension distinguishers, specifically distinguishing between dimensions 2 and 3 for a maximally entangled state.
The celebrated Clauser, Horne, Shimony and Holt (CHSH) game model helps to perform the security analysis of many two-player quantum protocols. This game specifies two Boolean functions whose outputs have to be computed to determine success or failure. It also specifies the measurement bases used by each player. In this paper, we generalize the CHSH game by considering all possible non-constant Boolean functions and all possible measurement basis (up to certain precision). Based on the success probability computation, we construct several equivalence classes and show how they can be used to generate three classes of dimension distinguishers. In particular, we demonstrate how to distinguish between dimensions 2 and 3 for a special form of maximally entangled state.