Multi-mode Gaussian State Analysis with Total Photon Counting

TL;DR

This paper investigates what properties of multimode Gaussian quantum states can be inferred from total photon number measurements using photon-number-resolving detectors, revealing that only the covariance matrix spectrum and displacements are determined.

Contribution

It provides a theoretical analysis showing that total photon number measurements reveal only specific properties of Gaussian states, such as the covariance matrix spectrum and displacements, in the ideal case.

Findings

Total photon number distribution determines the covariance matrix spectrum.

Displacements in each eigenspace are also determined.

For pure states, the spectrum reveals squeezing parameters.

Abstract

The continuing improvement in the qualities of photon-number-resolving detectors opens new possibilities for measuring quantum states of light. In this work we consider the question of what properties of an arbitrary multimode Gaussian state are determined by a single photon-number-resolving detector that measures total photon number. We find an answer to this question in the ideal case where the exact photon-number probabilities are known. We show that the quantities determined by the total photon number distribution are the spectrum of the covariance matrix, the absolute displacement in each eigenspace of the covariance matrix, and nothing else. In the case of pure Gaussian states, the spectrum determines the squeezing parameters.