Self-testing high dimensional states using the generalized magic square game

Understand

To date all self-tests for high dimensional systems are confined to many-qubit states.

• This is due to two restrictions in the literature: the standard techniques for proving self-testing results apply only to qubits, and there are few suitable non-local games that are known to require high dimensional non-qubit states to achieve their optimal quantum value.
• In this paper we address these two problems.
• Specifically, we generalize the usual self-testing framework to q$d$its and then apply it to a generalization of the magic square game, giving a self-test for two maximally entangled pairs of q$d$its.