Maximum-likelihood coherent-state quantum process tomography

TL;DR

This paper introduces a statistically based method for quantum process tomography using coherent states, leveraging quantum expectation-maximization to improve physical consistency and implementation simplicity.

Contribution

It presents a new csQPT technique based on quantum expectation-maximization that guarantees physicality and reduces experimental requirements.

Findings

Method successfully reconstructs process tensors from simulated data.

Incorporates a priori constraints for physically consistent results.

Requires fewer coherent states than previous methods.

Abstract

Coherent-state quantum process tomography (csQPT) is a method of completely characterizing a quantum-optical "black box" by probing it with coherent states and performing homodyne measurements on the output [M. Lobino et al, Science 322, 563 (2008)]. We present a technique for csQPT that is fully based on statistical inference, specifically, 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.