# Complete temporal mode characterization of non-Gaussian states by dual homodyne measurement

## TL;DR

This paper introduces a method using dual homodyne measurement to experimentally estimate the complex temporal-mode functions of non-Gaussian quantum states, including single and two-photon states, without prior state information.

## Contribution

It presents a novel, practical approach for directly estimating temporal-mode functions of non-Gaussian states without requiring prior knowledge or full state reconstruction.

## Key findings

- Successfully applied to experimentally created non-Gaussian states
- Can estimate TMFs of both single- and two-temporal-mode states
- Does not require prior state information or reconstruction

## Abstract

Optical quantum states defined in temporal modes, especially non-Gaussian states like photon-number states, play an important role in quantum computing schemes. In general, the temporal-mode structures of these states are characterized by one or more complex functions called temporal-mode functions (TMFs). Although we can calculate TMF theoretically in some cases, experimental estimation of TMF is more advantageous to utilize the states with high purity. In this paper, we propose a method to estimate complex TMFs. This method can be applied not only to arbitrary single-temporal-mode non-Gaussian states but also to two-temporal-mode states containing two photons. This method is implemented by continuous-wave (CW) dual homodyne measurement and doesn't need prior information of the target states nor state reconstruction procedure. We demonstrate this method by analyzing several experimentally created non-Gaussian states.