# Low-Loss High-Fidelity Frequency-Mode Hadamard Gates Based on Electromagnetically Induced Transparency

## TL;DR

This paper presents a high-efficiency, low-loss frequency-mode Hadamard gate and quantum frequency converter based on four-wave mixing in electromagnetically induced transparency, achieving record efficiencies and high fidelity for quantum communication.

## Contribution

The work introduces a novel four-wave mixing scheme for frequency-mode Hadamard gates with record efficiency and fidelity, advancing quantum photonic operations.

## Key findings

- Achieved 90% efficiency in frequency-mode Hadamard gate
- Achieved 84% efficiency in quantum frequency converter
- Fidelity of 0.99 in Hong-Ou-Mandel interference measurement

## Abstract

A frequency beam splitter (FBS) with the split ratio of 0.5 or 1 can be used as the frequency-mode Hadamard gate (FHG) for frequency-encoded photonic qubits or as the quantum frequency converter (QFC) for frequency up or down conversion of photons. Previous works revealed that all kinds of the FHG or QFC operating at the single-photon level had overall efficiency or output-to-input ratio around 50% or less. In this work, our FHG and QFC are made with the four-wave mixing process based on the dual-$\Lambda$ electromagnetically induced transparency scheme. We achieved an overall efficiency of 90$\pm$4% in the FGH and that of 84% in the QFC using coherent-state single photons, both of which are the best up-to-date records. To test the fidelity of the FBS, we propose a novel scheme of Hong-Ou-Mandel interference (HOMI) for quantum process tomography. The fidelity indicated by the HOMI's $g^{(2)}$ measurement of the FHG is 0.99$\pm$0.01. Such low-loss high-fidelity FHG and QFC or FBS with the tunable split ratio can lead to useful operations or devices in long-distance quantum communication.