Sequential measurements, disturbance and property testing
Aram Harrow, Massachusetts Institute of Technology
We describe two procedures which, given access to one copy of a quantum state and a sequence of two-outcome measurements, can distinguish between the case that at least one of the measurements accepts the state with high probability, and the case that all of the measurements have low probability of acceptance. The measurements cannot simply be tried in sequence, because early measurements may disturb the state being tested. One procedure is based on a variant of Marriott-Watrous amplification. The other procedure is based on the use of a test for this disturbance, which is applied with low probability.
We find a number of applications, including quantum query complexity separations, testing properties of quantum states and operations and composite hypothesis testing.
Based on
https://arxiv.org/abs/1607.03236 which is joint work with Cedric Lin and Ashley Montanaro.