Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optics Express

Preparation of heralded high-fidelity high-dimensional entangled states implemented with qudit-encoded photon systems

Ming Ma, Qiulin Tan, Fang‐Fang Du

Published May 13, 2025• 15 citations
Publisher

Abstract

Compared with traditional two-dimensional qubits, higher-dimensional qubits offer a larger state space for storing and processing information, which can manifest stronger non-classical correlations, simplify circuit complexity, reduce computational resources, and enhance loss tolerance in photon-based quantum information processing. To harness the potential, essential research on preparing qudit-based high-dimensional entangled states is necessary. In the paper, we propose the preparation procedure of arbitrary four-dimensional two-qudit entanglement and three-qudit entanglement for photon systems implemented with error-heralded quantum devices and controlled-not gates. Moreover, as the practical errors that grow out of defective photon scattering, i.e., coupling strength restriction of the quantum-dot-cavity system and cavity leakage imperfection, can be turned into the response of the single-photon detectors, the generation of arbitrary high-dimensional entanglement appears in an error-heralded way, and their fidelities are robust, enhancing experimental accessibility.

DOI
10.1364/oe.561002

Related papers

Heralded qudit-based high-dimensional entanglement generation for hybrid photon-emitter system by waveguide-mediated scattering

Fang‐Fang Du, Ling‐Hui Li, Qiu-Lin Tan +1 more

Quantum entanglement systems based on qudits dilate high-dimensional (HD) state spaces and enhance resistance to loss in quantum information processing (QIP). To fully exploit this potential, effective schemes for generating HD entanglement are crucial. In this paper, we propose a flexible heralded scheme generating random four-dimensional (4D) two-qudit maximal entanglement for a hybrid photon-emitter system by entering different input ports. This approach can be further extended to prepare 4D $n$-qudit $(n\ensuremath{\ge}3)$ maximal entanglement utilizing the 4D single-qudit ${Z}^{m}(m=1,2,3)$ gate for the first qudit and ${X}^{m}$ gate for the other qudits (except the second qudit). For the hybrid system, the first 4D qudit is encoded on the hybrid polarization-path states of a flying photon, while the second and subsequent 4D qudits are represented by two stationary emitters coupled to the respective 1D waveguide. The qudit-encoded hybrid HD entanglement offers advantages over economizing quantum resource without any auxiliary qudits and obtaining robust fidelities of various HD entanglement by the error-detected mechanism of the emitter-waveguide systems. Moreover, the proposed protocol can be spread to generate $d\mathrm{D}$ $n$-qudit $(d\ensuremath{\ge}{2}^{p+1},$ $n,p=2,3,\ensuremath{\cdots})$ entangled states, further broadening its applicability in HD QIP.

arXiv:2504.07386•Physical Review A•Nov 21, 2025•4 citations

Error-heralded high-dimensional quantum gate with robust fidelity

Fang‐Fang Du, Xue-Mei Ren, Jing Guo

Quantum computing in high-dimensional spaces holds promise for a plethora of applications, i.e., handling more intricate information and executing wider quantum operations, in complex quantum information technologies (QITs). In the paper, we set up an error-heralded, resource-saving, circuit-simplified, and 4×4-dimensional controlled-not (CNOT) gate, where the polarized and spatial state of the flying photon (i.e., the control qudit) can effectively control the collective spin wave state of two atomic ensembles (i.e., the target qudit) in two double-sided cavities. Moreover, through meticulous analysis, the feasibility of the high-dimensional gate using existing technology boasts the exceptional performance including a near-unity fidelity and high efficiency exceeding 0.95, in principle, as the undesired performances originated from the little side leakage and the finite coupling strength, and the imperfect atom-ensemble-cavity interactions are heralded by single-photon detectors. Besides, auxiliary photons or atomic ensembles are unnecessary. Therefore, our protocol stands out for its simplicity, efficient resource utilization, and real-time error prediction, contributing significantly to the efficacy of QIT and charting a promising path towards the realization of high-dimensional quantum computing endowed with heightened capabilities.

Optics Express•Aug 9, 2024•30 citations

Heralded fidelity-robust high-dimensional quantum computing

Fang‐Fang Du, Zhi‐Guo Fan, Zhuoya Bai +1 more

Abstract In high-dimensional quantum systems, qudits offer a richer resource than traditional two-dimensional qubits, increasing the capacity of quantum channels and enhancing the efficiency of fault-tolerant quantum computation. These advantages can be utilized to solve complex problems across various fields. In the paper, we propose a 2-qudit controlled-NOT (CNOT) gate in a 4 × 4 -dimensional space and a 3-qudit controlled-controlled-NOT (Toffoli) gate in a 4 × 4 × 4 -dimensional space, both equipped with error-heralded units. Our designs do not require auxiliary photons or extra negatively charged nitrogen-vacancy (NV−) center, resulting in saving resources. Moreover, since the imperfect NV−-cavity interaction processes are predicted in real-time by sensitive single-photon detectors, both high-dimensional CNOT and Toffoli gates boast robust fidelities using existing technology. Furthermore, our protocols simplify circuits with error-heralded units, significantly contributing to the effectiveness of quantum information technology and paving the way for advanced high-dimensional quantum computing.

New Journal of Physics•Jun 24, 2025•9 citations

Generation of arbitrary high-dimensional qudit-based entangled states

Fang‐Fang Du, Ming Ma, Zhuoya Bai +1 more

The generation of a high-dimensional quantum entangled state provides a crucial resource for achieving more complex and diverse quantum information processing tasks. In this paper, we present two deterministic protocols designed for the generation of a four-dimensional two-qudit Bell state and three-qudit Greenberger-Horne-Zeilinger (GHZ) state assisted by cross-Kerr nonlinearity, where the four-dimensional qudit is encoded in the hybrid polarization-spatial state of the single photon to conserve quantum resources and alleviate environmental noise. The proposed protocols for generating a four-dimensional two-qudit Bell state and three-qudit GHZ state are circuit concise, high success, robust fidelity, noise resistant, and resource saving. Moreover, the four-dimensional $N$-qudit ($N>3$) GHZ states can be generated with the help of the $N\ensuremath{-}1$ generating devices of the four-dimensional Bell state. Consequently, its efficiency and fidelity decay exponentially by a factor of $N\ensuremath{-}1$. Further, the arbitrary high-dimensional qudit-encoded entangled states can be achieved with linear-optics four-dimensional single-qudit $X$ gates and $Z$ gates. These protocols offer a reference for further advancements in high-dimensional state generation technology and providing insights for the practical implementations of metrological enhancement, quantum simulation, high-dimensional quantum computation, and quantum error correction.

Physical Review A•Mar 6, 2025•33 citations

Kerr‐Effect‐Based High‐Dimensional Entanglement Generation for Qudit Systems

Ming Ma, Qiang Zhu, Fang‐Fang Du

Abstract Employing high‐dimensional photonic encodings (qudits) instead of the traditional 2D encodings (qubits) can significantly enhance loss tolerance and reduce computational resources in photon‐based quantum information technology (QIT). To tap into this potential, effective schemes for the high‐dimensional generation of entangled states are essential. In this study, two arbitrary 4D entanglement generation protocols based on cross‐Kerr effect are developed, including two‐qudit entangled states with two photon pairs and three‐qudit entangled states with three photon pairs. These 4D entangled states require neither auxiliary photons (or entangled states) nor complicated quantum circuits. The success probabilities of high‐dimensional entangled states are close to 1 and their fidelities are robust against the photon loss with the current technology. The 4D entangled states depend on only simple linear‐optics elements, available four‐dimensional single‐qudit operations, and mature measurement methods, making our proposed protocols feasible and efficient in practical QIT.

Advanced Quantum Technologies•Apr 8, 2025•12 citations

Efficient High-Dimensional Entangled State Analyzer with Linear Optics

Niv Bharos, Liubov A. Markovich, Johannes Borregaard

The use of higher-dimensional photonic encodings (qudits) instead of two-dimensional encodings (qubits) can improve the loss tolerance and reduce the computational resources of photonic-based quantum information processing. To harness this potential, efficient schemes for entangling operations such as the high-dimensional generalization of a linear optics Bell measurement will be required. We show how an efficient high-dimensional entangled state analyzer can be implemented with a linear optics interferometer and auxiliary photonic states. The degree of entanglement of the auxiliary state is much less than in previous protocols as quantified by an exponentially smaller Schmidt rank. In addition, the auxiliary state only occupies a single spatial mode, allowing it to be generated deterministically from a single quantum emitter coupled to a small qubit register. The reduced complexity of the auxiliary states results in a high robustness to imperfections and we show that auxiliary states with fidelities above 0.9 for qudit dimensions 4 can be generated in the presence of qubit error rates on the order of 10%. This paves the way for experimental demonstrations with current hardware.

arXiv:2401.15066•Quantum•Apr 18, 2025•7 citations
Compared with traditional two-dimensional qubits, higher-dimensional qubits offer a larger state space for storing and processing information, which can manifest stronger non-classical correlations, simplify circuit complexity, reduce computational resources, and enhance loss tolerance in photon-based quantum information processing. To harness the potential, essential research on preparing qudit-based high-dimensional entangled states is necessary. In the paper, we propose the preparation procedure of arbitrary four-dimensional two-qudit entanglement and three-qudit entanglement for photon systems implemented with error-heralded quantum devices and controlled-not gates. Moreover, as the practical errors that grow out of defective photon scattering, i.e., coupling strength restriction of the quantum-dot-cavity system and cavity leakage imperfection, can be turned into the response of the single-photon detectors, the generation of arbitrary high-dimensional entanglement appears in an error-heralded way, and their fidelities are robust, enhancing experimental accessibility.
Quantum entanglement systems based on qudits dilate high-dimensional (HD) state spaces and enhance resistance to loss in quantum information processing (QIP). To fully exploit this potential, effective schemes for generating HD entanglement are crucial. In this paper, we propose a flexible heralded scheme generating random four-dimensional (4D) two-qudit maximal entanglement for a hybrid photon-emitter system by entering different input ports. This approach can be further extended to prepare 4D nnn-qudit $(n\ensuremath{\ge}3)$ maximal entanglement utilizing the 4D single-qudit Zm(m=1,2,3){Z}^{m}(m=1,2,3)Zm(m=1,2,3) gate for the first qudit and Xm{X}^{m}Xm gate for the other qudits (except the second qudit). For the hybrid system, the first 4D qudit is encoded on the hybrid polarization-path states of a flying photon, while the second and subsequent 4D qudits are represented by two stationary emitters coupled to the respective 1D waveguide. The qudit-encoded hybrid HD entanglement offers advantages over economizing quantum resource without any auxiliary qudits and obtaining robust fidelities of various HD entanglement by the error-detected mechanism of the emitter-waveguide systems. Moreover, the proposed protocol can be spread to generate dDd\mathrm{D}dD nnn-qudit $(d\ensuremath{\ge}{2}^{p+1},$ $n,p=2,3,\ensuremath{\cdots})$ entangled states, further broadening its applicability in HD QIP.
Quantum computing in high-dimensional spaces holds promise for a plethora of applications, i.e., handling more intricate information and executing wider quantum operations, in complex quantum information technologies (QITs). In the paper, we set up an error-heralded, resource-saving, circuit-simplified, and 4×4-dimensional controlled-not (CNOT) gate, where the polarized and spatial state of the flying photon (i.e., the control qudit) can effectively control the collective spin wave state of two atomic ensembles (i.e., the target qudit) in two double-sided cavities. Moreover, through meticulous analysis, the feasibility of the high-dimensional gate using existing technology boasts the exceptional performance including a near-unity fidelity and high efficiency exceeding 0.95, in principle, as the undesired performances originated from the little side leakage and the finite coupling strength, and the imperfect atom-ensemble-cavity interactions are heralded by single-photon detectors. Besides, auxiliary photons or atomic ensembles are unnecessary. Therefore, our protocol stands out for its simplicity, efficient resource utilization, and real-time error prediction, contributing significantly to the efficacy of QIT and charting a promising path towards the realization of high-dimensional quantum computing endowed with heightened capabilities.
Abstract In high-dimensional quantum systems, qudits offer a richer resource than traditional two-dimensional qubits, increasing the capacity of quantum channels and enhancing the efficiency of fault-tolerant quantum computation. These advantages can be utilized to solve complex problems across various fields. In the paper, we propose a 2-qudit controlled-NOT (CNOT) gate in a 4 × 4 -dimensional space and a 3-qudit controlled-controlled-NOT (Toffoli) gate in a 4 × 4 × 4 -dimensional space, both equipped with error-heralded units. Our designs do not require auxiliary photons or extra negatively charged nitrogen-vacancy (NV−) center, resulting in saving resources. Moreover, since the imperfect NV−-cavity interaction processes are predicted in real-time by sensitive single-photon detectors, both high-dimensional CNOT and Toffoli gates boast robust fidelities using existing technology. Furthermore, our protocols simplify circuits with error-heralded units, significantly contributing to the effectiveness of quantum information technology and paving the way for advanced high-dimensional quantum computing.
The generation of a high-dimensional quantum entangled state provides a crucial resource for achieving more complex and diverse quantum information processing tasks. In this paper, we present two deterministic protocols designed for the generation of a four-dimensional two-qudit Bell state and three-qudit Greenberger-Horne-Zeilinger (GHZ) state assisted by cross-Kerr nonlinearity, where the four-dimensional qudit is encoded in the hybrid polarization-spatial state of the single photon to conserve quantum resources and alleviate environmental noise. The proposed protocols for generating a four-dimensional two-qudit Bell state and three-qudit GHZ state are circuit concise, high success, robust fidelity, noise resistant, and resource saving. Moreover, the four-dimensional NNN-qudit (N>3N>3N>3) GHZ states can be generated with the help of the $N\ensuremath{-}1$ generating devices of the four-dimensional Bell state. Consequently, its efficiency and fidelity decay exponentially by a factor of $N\ensuremath{-}1$. Further, the arbitrary high-dimensional qudit-encoded entangled states can be achieved with linear-optics four-dimensional single-qudit XXX gates and ZZZ gates. These protocols offer a reference for further advancements in high-dimensional state generation technology and providing insights for the practical implementations of metrological enhancement, quantum simulation, high-dimensional quantum computation, and quantum error correction.
Abstract Employing high‐dimensional photonic encodings (qudits) instead of the traditional 2D encodings (qubits) can significantly enhance loss tolerance and reduce computational resources in photon‐based quantum information technology (QIT). To tap into this potential, effective schemes for the high‐dimensional generation of entangled states are essential. In this study, two arbitrary 4D entanglement generation protocols based on cross‐Kerr effect are developed, including two‐qudit entangled states with two photon pairs and three‐qudit entangled states with three photon pairs. These 4D entangled states require neither auxiliary photons (or entangled states) nor complicated quantum circuits. The success probabilities of high‐dimensional entangled states are close to 1 and their fidelities are robust against the photon loss with the current technology. The 4D entangled states depend on only simple linear‐optics elements, available four‐dimensional single‐qudit operations, and mature measurement methods, making our proposed protocols feasible and efficient in practical QIT.
The use of higher-dimensional photonic encodings (qudits) instead of two-dimensional encodings (qubits) can improve the loss tolerance and reduce the computational resources of photonic-based quantum information processing. To harness this potential, efficient schemes for entangling operations such as the high-dimensional generalization of a linear optics Bell measurement will be required. We show how an efficient high-dimensional entangled state analyzer can be implemented with a linear optics interferometer and auxiliary photonic states. The degree of entanglement of the auxiliary state is much less than in previous protocols as quantified by an exponentially smaller Schmidt rank. In addition, the auxiliary state only occupies a single spatial mode, allowing it to be generated deterministically from a single quantum emitter coupled to a small qubit register. The reduced complexity of the auxiliary states results in a high robustness to imperfections and we show that auxiliary states with fidelities above 0.9 for qudit dimensions 4 can be generated in the presence of qubit error rates on the order of 10%. This paves the way for experimental demonstrations with current hardware.