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

Quantum 8, 1405 (2024).

https://doi.org/10.22331/q-2024-07-10-1405

We propose an estimation procedure for $d$-dimensional unitary transformations. For $dgt2$, 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.