Hi all,
today we have a visitor, Karl Mayer, from Manny Knill's group at the University of Colorado. Karl will give a ~1/2 hour talk about his research on tomography at 2pm in E41.1. See below for the title and abstract.
Best,
-joe
Paper: https://arxiv.org/abs/1805.04491 Title: Quantum Process Fidelity Bounds from Sets of Input States Abstract: We investigate the problem of bounding the quantum process fidelity given bounds on the fidelities between target states and the action of a process on a set of pure input states. We formulate the problem as a semidefinite program and prove convexity of the minimum process fidelity as a function of the errors on the output states. We characterize the conditions required to uniquely determine a process in the case of no errors, and derive a lower bound on its fidelity in the limit of small errors for any set of input states satisfying these conditions. We then consider sets of input states whose one-dimensional projectors form a symmetric positive operator-valued measure (POVM). We prove that for such sets the minimum fidelity is bounded by a linear function of the average output state error. The minimal non-orthogonal symmetric POVM contains d+1 states, where d is the Hilbert space dimension. Our bounds applied to these states provide an efficient method for estimating the process fidelity without the use of full process tomography.