From particle counting to Gaussian tomography

TL;DR

This paper presents a method for complete quantum state and channel tomography of Gaussian states using particle counting, linking expectation values of number operators to all state parameters.

Contribution

It introduces a novel approach to Gaussian state and channel tomography based on particle counting, enabling complete characterization from number operator expectations.

Findings

Complete tomography of n-mode Gaussian states achieved

Method applies to Gaussian channels via coherent state outputs

Highlights challenges in number operator distribution and tomography complexity

Abstract

All the $n(2n+3)$ mean and covariance parameters of an $n$-mode Gaussian states are expressed in terms of the expectation values of the same number of conjugates of the total number observable. This permits a complete tomography of the state. The same is applied to outputs of a Gaussian channel corresponding to selected coherent states to perform the complete tomography of the channel. This leads to some interesting problems concerning the distribution of the number operator and also tomographic complexity.