# Time-resolved certification of frequency-bin entanglement over multi-mode channels

## TL;DR

This paper introduces a passive method to analyze frequency-bin entangled photons for scalable quantum communication, suitable for satellite and mobile systems.

## Contribution

A novel passive technique for processing frequency-encoded photons using linear interferometry and time-resolved detection is introduced.

## Key findings

- A CHSH inequality violation of ∣S∣ = 2.32 ± 0.05 is reported for frequency-bin entangled photons over multi-mode fiber.
- Quantum state tomography achieved a fidelity of up to 91% using time-resolved detection and energy-correlation measurements.
- Non-classical states were confirmed via violations of time-energy entropic uncertainty relations.

## Abstract

Frequency-bin entangled photons can be efficiently produced on-chip which offers a scalable, robust and low-footprint platform for quantum communication, particularly well-suited for resource-constrained settings such as mobile or satellite-based systems. However, analyzing such entangled states typically requires active and lossy components, limiting scalability and multi-mode compatibility. We demonstrate a novel technique for processing frequency-encoded photons using linear interferometry and time-resolved detection. Our approach is fully passive and compatible with spatially multi-mode light, making it suitable for free-space and satellite-to-ground applications. As a proof-of-concept, we utilize frequency-bin entangled photons generated from a high-brightness multi-resonator source integrated on-chip to show the ability to perform arbitrary projective measurements over both single- and multi-mode channels. We report the first measurement of the joint temporal intensity between frequency-bin entangled photons, which allows us to certify entanglement by violating the Clauser-Horne-Shimony-Holt (CHSH) inequality, with a measured value of ∣S∣ = 2.32 ± 0.05 over multi-mode fiber. By combining time-resolved detection with energy-correlation measurements, we perform full quantum state tomography, yielding a state fidelity of up to 91%. We further assess our ability to produce non-classical states via a violation of time-energy entropic uncertainty relations and investigate the feasibility of a quantum key distribution protocol. Our work establishes a resource-efficient and scalable approach toward the deployment of robust frequency-bin entanglement over free-space and satellite-based links.