  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. This self-test has two parties, perfect completeness for honest
quantum players, and requires only a constant number of measurement settings,
regardless of the dimension $d$.
