Abstract
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 such as 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.
