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Annalen der Physik

Deterministic Conversion of Hyperentangled States with Error‐Heralded Quantum Units

Fang‐Fang Du, Ming Ma, Xue‐Mei Ren, Gang Fan, Xin‐Shan Du, Linghui Li, Zhi‐Guo Fan, Jing Guo

Published Jan 7, 2024• 8 citations
Publisher

Abstract

Abstract In the paper, the possibility of two complete conversions is investigated, one is from the two‐photon hyperentangled Knill–Laflamme–Milburn (KLM) state to hyperentangled Bell states, the other is from three‐photon KLM state to the hyperentangled Greenberger–Horne–Zeilinger states, for photonic systems hyper‐encoded in polarization and spatial degrees of freedom assisted by error‐heralded quantum units (EHQUs). The system inhomogeneity and/or the imperfect photon scattering often restrict the performance of effective conversions of two types of hyperentangled states, and result in the reductions of the fidelity and the efficiency in tangible quantum information technologies. The polarization EHQU and spatial EHQU are two critical tools for actualizing two hyperentangled conversions in a heralded way, as the errors stemming from the system inhomogeneity and practically imperfect scattering are converted into efficacious responses of the detectors in our protocols. Thus, the fidelities of these conversion cases keep unchanged and have close to unity fidelities, which deepen the understanding of the properties of hyperentanglement.

DOI
10.1002/andp.202300455

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Annalen der Physik•Oct 1, 2018•15 citations
Abstract In the paper, the possibility of two complete conversions is investigated, one is from the two‐photon hyperentangled Knill–Laflamme–Milburn (KLM) state to hyperentangled Bell states, the other is from three‐photon KLM state to the hyperentangled Greenberger–Horne–Zeilinger states, for photonic systems hyper‐encoded in polarization and spatial degrees of freedom assisted by error‐heralded quantum units (EHQUs). The system inhomogeneity and/or the imperfect photon scattering often restrict the performance of effective conversions of two types of hyperentangled states, and result in the reductions of the fidelity and the efficiency in tangible quantum information technologies. The polarization EHQU and spatial EHQU are two critical tools for actualizing two hyperentangled conversions in a heralded way, as the errors stemming from the system inhomogeneity and practically imperfect scattering are converted into efficacious responses of the detectors in our protocols. Thus, the fidelities of these conversion cases keep unchanged and have close to unity fidelities, which deepen the understanding of the properties of hyperentanglement.
As the hyperentanglement of photon systems holds lots of remarkable applications for enhancing channel capacity with less quantum resource, the interconversion of various hyperentangled states warrants in-depth investigation and becomes a vital work for quantum information technologies. Here we realize completely mutual conversions between spatial-polarization hyperentangled Knill-Laflamme-Milburn state and hyperentangled W state for three-photon systems, resorting to hyperparallel quantum control gates and the practical nonlinear interaction of nitrogen-vacancy centers coupled with whispering-gallery-mode microresonators. The hyperparallel quantum gates, i.e., hyperparallel controlled-not and controlled-swap gates, are fundamental prerequisites for realizing interconversions of two hyperentangled states in a deterministic way. The fidelities of these conversion processes are robust and their efficiencies are also high due to fewer nonlinear interactions and errors heralded by the response of detectors, which intensify comprehending the properties of hyperentanglement.
Abstract Schemes for converting photonic polarized‐entangled Knill–Laflamme–Milburn (KLM) states to Greenberger–Horne–Zeilinger (GHZ) states are proposed using weak cross‐Kerr nonlinearity and X‐quadrature homodyne measurement. Analyses show that the two‐qubit (Bell state) and three‐qubit conversion cases have very high fidelities and close‐to‐unity probabilities. The conversion processes are robust against photon loss. The schemes linking these two entangled states may be helpful to the study of quantum information processing based on them.
Abstract Quantum entanglement plays a crucial role in quantum information technologies. In the paper, we propose two schemes to convert from two-photon Knill–Laflamme–Milburn (KLM) entangled states to Bell states and three-photon KLM state to Greenberger–Horne–Zeilinger states based on error-detected quantum devices (EDQDs), which employ the interaction between a quantum-dot-cavity system and a photon. Moreover, the quantum circuits of EDQDs applied in the conversion processes make our schemes carry out faithfully, as the practical photon-scattering deviations are changed into heralded-failure detections. Analyses show that conversion cases have unity fidelities and high efficiencies, which encourage us to appreciate deeply fundamental properties of entanglement.
Abstract Hybrid entangled states are crucial in quantum physics, offering significant benefits for hybrid quantum communication and quantum computation, and then the conversion of hybrid entangled states is equally critical. This paper presents two novel schemes, that is, one converts the two-qubit hybrid Knill–Laflamme–Milburn (KLM) entangled state into Bell states and the other one transforms the three-qubit hybrid KLM state into Greenberger–Horne–Zeilinger (GHZ) states assisted by error-predicted and parity-discriminated devices. Importantly, the integration of single photon detectors into the parity-discriminated device enhances predictive capabilities, mitigates potential failures, and facilitates seamless interaction between the nitrogen-vacancy center and photons, so the two protocols operate in an error-predicted way, improving the experimental feasibility. Additionally, our schemes demonstrate robust fidelities (close to 1) and efficiencies, indicating their feasibility with existing technology.
Abstract The interconversion of different types of entangled states not only can realize the information transmission but also play a significant role in quantum information technologies, including increasing scalability and computational power, and reducing error rates. Here, two protocols for achieving a complete interconversion between W state and Knill–Laflamme–Milburn state assisted by the quantum dot (QD)‐cavity systems and common quantum control gates are proposed. In particular, the protocols employ a heralded approach strategically designed to predict potential failures and facilitate seamless interaction between the QD‐cavity system and photons with the help of a single photon detectors, enhancing experimental accessibility. Through extensive analyzes and evaluations of two protocols, the proposed two protocols achieve remarkable utilization rates of photons (i.e., unit in principle) and achieve near‐unit fidelities and high efficiencies in principle.
Abstract Herein, two proposals are speculated to realize mutual conversions between Knill–Laflamme–Milburn (KLM) and W entangled states via X homodyne measurement (HM). By one of these proposals three‐qubit mutual conversions can be realized between these two photonic polarization entangled states. The other can be generalized to convert an arbitrary‐qubit KLM state to a W state adopting a control‐NOT gate. With the increasing number of qubits, the utilization ratio of photons in the second proposal would be close to unity. Analyses of the three‐qubit mutual conversions show that the proposal has a low error rate and high utilization ratio of photons. Moreover, the fidelity can also be very high even in consideration of decoherence. The P homodyne measurement is analyzed as well to improve the precision. The proposals, especially the second one, are expected to be helpful to reveal the relationship between these two robust multiple‐qubit entanglements.