CPT stands for charge conjugation, parity and time reversal. The field theories that we know, love and use so extensively in physics are intrinsically invariant under CPT transformations. The resulting prediction is that the electron and positron would have magnetic moments that have the same magnitude but an opposite sign. Must this prediction, based upon the CPT theorem which field theories obey, be true? Most of us in physics assume so. However, it is not yet clear that field theories have a universal application insofar as no attempt to use field theories to describe gravity has yet succeeded.
Because we can measure the electron (and presumably the positron) magnetic moment so much more accurately than can most anything else in physics it is irresistible to measure and compare these magnetic moments as a test whether CPT invariance holds in the simple and fundamental lepton system. To date, the most stringent test of CPT invariance with a lepton system is the UW comparison of the electron and positron magnetic moment*.
Our new quantum methods to measure the electron magnetic moment resulted in a 2008 measurement of the electron (but not yet the positron) magnetic moment that is about 15 times more accurate. For her thesis work Shannon Fogwell is building a new apparatus in which we hope to compare the positron and electron magnetic moments at our 3 ppt measurement uncertainty realized in 2008, or even better.
*R.S. Van Dyke, Jr., P.B. Schwinberg, and H.G. Dehmelt, Phys. Rev. Lett. 59, 26 (1987)