Bounding the quantum process fidelity with a minimal set of input states

Presenting Author: Karl Mayer, National Institute of Standards and Technology, Boulder
Contributing Author(s): Emanuel Knill

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. Finally, we introduce a set of d+1 pure states in d dimensions which form a minimal symmetric POVM. We prove that for this set of input states the minimum fidelity scales linearly with the average output state error, providing an efficient method for estimating the process fidelity without the use of full process tomography.

(Session 9b : Friday from 3:45pm-4:15pm)


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