Self-testing a multipartite quantum state means verifying
the existence of the state based on the outcomes of unknown or untrusted
measurements.

This concept is important in device-independent quantum
cryptography.

There are some previously known results on self-testing
which involve nonlocal binary XOR games such as the CHSH test and the GHZ
paradox.  In our work we expand on these
results.  We provide a general criterion
which, when satisfied, guarantees that a given nonlocal binary XOR game is a
robust self-test.  The error term in this
result is quadratic, which is the best possible.  In my talk I will explain the conceptual
basis for the criterion and offer some examples.  This is joint work with Yaoyun Shi
(arXiv:1207.1819).