Two-detector reconstruction of multiphoton states in linear optical networks

TL;DR

This paper introduces a resource-efficient method for partial reconstruction of multiphoton states in large linear optical networks using only two photon-number-resolving detectors, leveraging DQC1 circuits and maximum likelihood estimation.

Contribution

It presents a novel approach combining DQC1 circuits and MLE for efficient partial state reconstruction with minimal detector requirements in large-scale LONs.

Findings

Reduces detector count from M to 2 in state reconstruction

Demonstrates robustness against interferometer noise

Achieves efficient partial state characterization in simulations

Abstract

We propose a method for partial state reconstruction of multiphoton states in multimode ($N$-photon $M$-mode) linear optical networks (LONs) employing only two bucket photon-number-resolving (PNR) detectors. The reconstructed Heisenberg-Weyl-reduced density matrix captures quantum coherence and symmetry with respect to Heisenberg-Weyl operators. Employing deterministic quantum computing with one qubit (DQC1) circuits, we reduce the detector requirement from $M$ to $2$, while the requirement on measurement configurations is retained $2M^{3}-2M$. To ensure physicality, maximum likelihood estimation (MLE) is incorporated into the DQC1 reconstruction process, with numerical simulations demonstrating the efficiency of our approach and its robustness against interferometer noises. This method offers a resource-efficient solution for state characterization in large-scale LONs to advance photonic quantum technologies.