Estimation of high-dimensional unitary transformations saturating the Quantum Cramér-Rao bound

Abstract

We propose an estimation procedure for d-dimensional unitary transformations. For d>2, the unitary transformations close to the identity are estimated saturating the quantum Cramér-Rao bound. For d=2, the estimation of all unitary transformations is also optimal with some prior information. We show through numerical simulations that, even in the absence of prior information, two-dimensional unitary transformations can be estimated with greater precision than by means of standard quantum process tomography.