Maximum-likelihood coherent-state quantum process tomography

Abstract

Coherent-state quantum process tomography (csQPT) is a method for completely characterizing a quantum-optical ‘black box’ by probing it with coherent states and carrying out homodyne measurements on the output (Lobino et al 2008 Science 322 563). We present a technique for csQPT that is fully based on statistical inference, in particular, quantum expectation-maximization. The method relies on the Jamiolkowski isomorphism and iteratively reconstructs the process tensor in the Fock basis directly from the experimental data. This approach permits incorporation of a priori constraints into the reconstruction procedure, thereby guaranteeing that the resulting process tensor is physically consistent. Furthermore, our method is easier to implement and requires a narrower range of coherent states than its predecessors. We test its feasibility using simulations on several experimentally relevant processes.