Position and momentum tomography

TL;DR

This paper demonstrates how the statistical method of moments can be used to reconstruct position and momentum distributions of quantum objects from single measurement data across three models, applicable to a broad class of initial states.

Contribution

It introduces the application of the method of moments to quantum state tomography for position and momentum, covering multiple measurement models.

Findings

Method of moments successfully reconstructs distributions for various models.

Applicable to a large class of initial states with exponential boundedness.

Provides a unified approach for different measurement schemes.

Abstract

We illustrate the use of the statistical method of moments for determining the position and momentum distributions of a quantum object from the statistics of a single measurement. The method is used for three different, though related, models; the sequential measurement model, the Arthurs-Kelly model and the eight-port homodyne detection model. In each case, the method of moments gives the position and momentum distribution for a large class of initial states, the relevant condition being the exponential boundedness of the distributions.