By harnessing multiple degrees of freedom (DoFs) within a single photon, controlled quantum unitaries, such as the two-qubit controlled-NOT (CNOT) gate, play a pivotal role in advancing quantum communication protocols like dense coding and entanglement distillation. In this work, we devise and realize a CNOT operation between polarization and frequency DoFs by exploiting directionally dependent electro-optic phase modulation within a fiber Sagnac loop. Alongside computational basis measurements, we validate the effectiveness of this operation through the synthesis of all four Bell states in a single photon, all with fidelities greater than 98%. This demonstration opens new avenues for manipulating hyperentanglement across these two crucial DoFs, marking a foundational step toward leveraging polarization-frequency resources in fiber networks for future quantum applications.
@article{arxiv.2404.07317,
title = {Building a controlled-NOT gate between polarization and frequency},
author = {Hsuan-Hao Lu and Joseph M. Lukens and Muneer Alshowkan and Brian T. Kirby and Nicholas A. Peters},
journal= {arXiv preprint arXiv:2404.07317},
year = {2024}
}