  Self-testing allows us to determine, through classical interaction only,
whether some players in a non-local game share particular quantum states. Most
work on self-testing has concentrated on developing tests for small states like
one pair of maximally entangled qubits, or on tests where there is a separate
player for each qubit, as in a graph state. Here we consider the case of
testing many maximally entangled pairs of qubits shared between two players.
Previously such a test was shown where testing is sequential, i.e., one pair is
tested at a time. Here we consider the parallel case where all pairs are tested
simultaneously, giving considerably more power to dishonest players. We derive
sufficient conditions for a self-test for many maximally entangled pairs of
qubits shared between two players and also two constructions for self-tests
where all pairs are tested simultaneously.
