Iterative maximum-likelihood reconstruction in quantum homodyne tomography

Abstract. I propose an iterative expectation maximization algorithm for reconstructing the density matrix of an optical ensemble from a set of balanced homodyne measurements. The algorithm applies directly to the acquired data, bypassing the intermediate step of calculating marginal distributions. The advantages of the new method are made manifest by comparing it with the traditional inverse Radon transformation technique. PACS numbers: 03.65.Wj, 42.50.Dv Submitted to: J. Opt. B: Quantum Semiclass. Opt. Quantum tomography is a technique of characterizing a state of a quantum system by subjecting it to a large number of quantum measurements, each time preparing the system anew. By varying the configuration of the measurement apparatus, one acquires the quantum statistics associated with different bases from which complete information about the state of the system can be extracted. The ensemble’s density matrix can be evaluated from the experimental statistical data by a number of techniques. In this paper we are dealing with one such technique,