High-dimensional entangled states have attracted attention because of their strong nonlocality and powerful capability for quantum information processing. By the methods presented in this paper, arbitrary forms-entangled qudits including symmetric and asymmetric forms could be generated with weak cross-Kerr nonlinearity. These schemes are heralded by the use of single-photon detectors. If all the detectors do not register any single photons, the generation is a success with the probability 1/nM determined by dimension n and partite M. Furthermore, these schemes work well even with the common photon number nonresolving detectors; therefore they are feasible with the current experimental technology.
High-dimensional entangled states have attracted attention because of their strong nonlocality and powerful capability for quantum information processing. By the methods presented in this paper, arbitrary forms-entangled qudits including symmetric and asymmetric forms could be generated with weak cross-Kerr nonlinearity. These schemes are heralded by the use of single-photon detectors. If all the detectors do not register any single photons, the generation is a success with the probability 1/nM determined by dimension n and partite M. Furthermore, these schemes work well even with the common photon number nonresolving detectors; therefore they are feasible with the current experimental technology.
In quantum information processing, quantum entanglement plays a very important role with special physical property, which makes the quantum information have many new characteristics that the classical information do not have, and provides a new physical resource in the transmission and processing of information. Compared with classical bit, quantum entanglement, especially the high dimensional quantum entanglement (i.e., entangled qudit), has a large information storage space and good security confidentiality, which means stronger nonlocality and much more powerful capability in quantum information processing. In this sense, here we focus on the topic of polarized entangled qudit generation, especially the asymmetric entangled qutrit generation, which hasnt been discussed before. The initial states could be an entangled photon pair and two single photons. Using two qubus beams as ancilla, and based on the cross phase modulation, the initial quantum states could be projected into different subspaces, which include the desired one. Finally, through the bi-photon Hong-Ou-Mandel interference, the asymmetric entangled qutrit could be generated. This scheme is heralded by the detection results of three ideal photon number non-resolving detectors (PNNDs). If neither of the three ideal PNNDs registers photons, the generation is successful; otherwise, any click appearing on one of the three ideal PNNDs means the failure of the generation. The corresponding success probability of maximally entangled qutrit generation is 3/64, which is relatively small. However, the success probability could be increased to 3/8 by using the special photon detectors, associated with the quantum non- demolition detectors (QNDs) replacing the ideal PNNDs. The more efficient scheme is still heralded, so the generated entangled qutrit could be used flexibly in the quantum information processing.
We propose methods for generating Bell-type entangled coherent states for quantum information processing. The protocols are completed using linear optical elements, single-photon detectors, and cross-Kerr nonlinearity. We investigate the decoherence effect on our protocols; photon loss is found to affect only the probability, not the fidelity, of the generation process. The entanglement of the generated entangled states is also analyzed using concurrence. Finally, the feasibility of our scheme is discussed using the continuous-time cross-phase modulation model. In the weak nonlinearity region, on the condition that θ2|αp|2∼1, θ≪1, and σ2≪1, our scheme is applicable theoretically.
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.
We propose a protocol for creating arbitrary qudit state (including entangled states) with arbitrary dimensionality in continuous variable system using weak cross-Kerr nonlinearity, linear beamsplitters, detectors not resolving photon numbers, and sources of coherent states. The equation for unique determination of the used coherent states amplitudes is found. The protocol is applicable for creating entangled states at distances of 100 km using cross-Kerr nonlinearity χ ≥ χ min ≃ 0.01 and optical fiber quantum channel.
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.
In this paper, we provide a simple but powerful module to generate entangled qudits. This module, assisted with cross-Kerr nonlinearity, is flexible for generation of entangled qudits with arbitrary dimensions. Since the generation is still probabilistic, we modify the simple module in order to increase efficiency and save resources. With the modified module, the input independent qudits could be transformed into different entangled forms, which include the possible maximal entangled form and the less entangled forms. The corresponding total success probability could reach 1.