Efficient Quantum Tomography of Two-Mode Wigner Functions

TL;DR

This paper presents a novel, efficient quantum tomography method for reconstructing two-mode Wigner functions using convex optimization and maximum entropy principles, enabling unbiased state estimation and entanglement quantification.

Contribution

It introduces a new quantum tomography approach combining convex optimization and maximum entropy, with a finite Fock basis representation for improved efficiency and entanglement analysis.

Findings

Efficient reconstruction of two-mode Wigner functions demonstrated.

Method allows unbiased state estimation via maximum entropy.

Entanglement can be easily quantified using the finite basis representation.

Abstract

We introduce an efficient method to reconstruct the Wigner function of many-mode continuous variable systems. It is based on convex optimization with semidefinite programs, and also includes a version of the maximum entropy principle, in order to yield unbiased states. A key ingredient of the proposed approach is the representation of the state in a truncated Fock basis. As a bonus, the discrete finite representation allows to easily quantify the entanglement.