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A single-photon polarization-frequency controlled-NOT gate

Hsuan‐Hao Lu, Joseph M. Lukens, Muneer Alshowkan, Brian T. Kirby, Nicholas A. Peters

Published Jan 1, 2025• 0 citations
Publisher

Abstract

We develop a high-fidelity controlled-NOT gate between photonic polarization and frequency, leveraging direction-dependent electro-optic phase modulation in a fiber Sagnac loop. This design could facilitate massively parallelizable entanglement distillation with polarization-frequency resources in lightwave networks.
DOI
10.1364/cleo_fs.2025.ff105_3

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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.
Frequency-bin encoding is massively parallelizable and robust for optical fiber transmission. When coupled with an additional degree of freedom (DoF), the expansion of the Hilbert space allows for deterministic controlled operations between two DoFs within a single photon. Such capabilities, when combined with photonic hyperentanglement, are of great value for quantum communication protocols, including dense coding and single-copy entanglement distillation. In this talk, we present an all-fiber-coupled, ultrabroadband polarization–frequency hyperentangled source and conduct comprehensive quantum state tomography across multiple dense wavelength division multiplexing channels spanning the optical C+L-band (1530–1625 nm). In addition, we design and implement a high-fidelity controlled-NOT (cnot) operation between polarization and frequency DoFs by exploiting electro-optic phase modulation within a fiber Sagnac loop. Collectively, our hyperentangled source and two-qubit gate should unlock new opportunities for harnessing polarization–frequency resources in established telecommunication fiber networks for future quantum applications.
Abstract The realization of strong photon–photon interactions has presented an enduring challenge across photonics, particularly in quantum computing, where two-photon gates form essential components for scalable quantum information processing (QIP). While linear-optic schemes have enabled probabilistic entangling gates in spatio-polarization encoding, solutions for many other useful degrees of freedom remain missing. In particular, no two-photon gate for the important platform of frequency encoding has been experimentally demonstrated, due in large part to the additional challenges imparted by the mismatched wavelengths of the interacting photons. In this article, we design and implement an entangling gate for frequency-bin qubits, a coincidence-basis controlled-NOT (CNOT), using line-by-line pulse shaping and electro-optic modulation. We extract a quantum unitary fidelity of 0.91 ± 0.01 via a parameter inference approach based on Bayesian machine learning, which enables accurate gate reconstruction from measurements in the two-photon computational basis alone. Our CNOT imparts a single-photon frequency shift controlled by the frequency of another photon—an important capability in itself—and should enable new directions in fiber-compatible QIP.
We report an experimental demonstration of a quantum controlled-NOT gate constructed entirely in optical fiber and operating on polarization-encoded single-photon qubits. We operated this gate using two heralded optical fiber single-photon sources and found an average logical fidelity of 90% and an average process fidelity of $0.83\ensuremath{\le}\overline{F}\ensuremath{\le}0.91$. On the basis of a simple model we are able to conclude that imperfections are primarily due to the photon sources, meaning that the gate itself works with very high fidelity. Such all fiber quantum information processing will likely have important applications in future quantum networks.
Fiber-based entangled photon sources are a key resource in emerging quantum technologies due to compactness, long-term stability and alignment-free operation. Fast control of the quantum state properties is also necessary in practical scenarios, where a universal source can be employed with different temporal and spectral configurations. Here, we report on a flexible source design that produces high-quality entanglement from continuous-wave up to GHz-pulsed operation modes. Our approach uses off-the-shelf optical components in a Sagnac configuration to generate polarization-entangled photon pairs at telecom wavelength. This design further allows phase modulation above MHz speeds with high fidelity. Together with its 60 nm spectral bandwidth, the proposed system is entirely suitable for wavelength-multiplexed and reconfigurable quantum networks, where state modulation or active bandwidth allocation is required.
We demonstrate a robust implementation of a deterministic linear-optical controlled-not gate for single-photon two-qubit quantum logic. A polarization Sagnac interferometer with an embedded 45 degrees -oriented dove prism is used to enable the polarization control qubit to act on the momentum (spatial) target qubit of the same photon. The optical controlled-not gate requires no active stabilization because the two spatial modes share a common path, and it is used to entangle the polarization and momentum qubits.