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Annalen der Physik

Conversion of Knill–Laflamme–Milburn Entanglement to Greenberger–Horne–Zeilinger Entanglement in Decoherence‐Free Subspace

Lei Chen, Xiao‐Ming Xiu, Li Dong, Shou Zhang, Shi‐Lei Su, Shu Chen, Erjun Liang

Published Nov 21, 2021• 10 citations
Publisher

Abstract

Abstract In the process of quantum information processing, decoherence effect caused by the coupling between system and its environment will no doubt lead to the error of quantum information stored in the system. To decrease the influence of decoherence effect, decoherence‐free subspace (DFS) is introduced. In this work, several schemes to convert the polarized‐entangled Knill–Laflamme–Milburn (KLM) states into Greenberger–Horne–Zeilinger (GHZ) states in DFS by using the weak cross‐Kerr nonlinearity are proposed. Numerical analysis shows that the proposed schemes have high fidelity and success probability. Due to the unique applications of multi‐qubit quantum entangled states in quantum information processing and the robust feature of DFS, the proposed schemes may play positive roles in the future development of quantum communication and quantum information processing tasks.

DOI
10.1002/andp.202100365

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Abstract In the process of quantum information processing, decoherence effect caused by the coupling between system and its environment will no doubt lead to the error of quantum information stored in the system. To decrease the influence of decoherence effect, decoherence‐free subspace (DFS) is introduced. In this work, several schemes to convert the polarized‐entangled Knill–Laflamme–Milburn (KLM) states into Greenberger–Horne–Zeilinger (GHZ) states in DFS by using the weak cross‐Kerr nonlinearity are proposed. Numerical analysis shows that the proposed schemes have high fidelity and success probability. Due to the unique applications of multi‐qubit quantum entangled states in quantum information processing and the robust feature of DFS, the proposed schemes may play positive roles in the future development of quantum communication and quantum information processing tasks.
Several schemes are proposed to realize the conversion of photonic polarized-entangled Greenberger-Horne-Zeilinger state to Knill-Laflamme-Milburn state in decoherence-free subspace (DFS) via weak cross-Kerr nonlinearity and X-quadrature homodyne measurement with high fidelity. DFS is introduced to decrease the decoherence effect caused by the coupling between the system and the environment. Optimizations to improve the success rate and utilization of residual states are further investigated. This study indicates important applications for quantum information processing in the future.
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 Mutual conversions between different entangled states play a significant role in quantum information processing (QIP), significantly boosting the versatility and robustness of quantum systems, and particularly paving the way for demanding specific entanglement forms. Reliable protocols are proposed for the deterministic mutual conversions between the three‐logic‐qubit W state and the three‐logic‐qubit Knill–Laflamme–Milburn state within a decoherence‐free subspace (DFS), which utilizes weak cross‐Kerr nonlinearity combined with X‐homodyne measurement. In‐depth analyses of both protocols confirm that they can achieve high fidelities and outstanding efficiencies by related feedback operations. Additionally, the protocols effectively suppress decoherence effects through the use of DFS, enabling the advanced development of practical QIP.
The Knill-Laflamme-Milburn (KLM) entangled state, proposed by Knill et al. in Nature409, 46 (2001)NATUAS0028-083610.1038/35051009, has unique advantages for linear optics quantum information processing tasks, because it is able to decrease the error rate. In this paper, we propose scalable schemes to generate the multi-qubit KLM entangled states with single-photon resources and weak cross-Kerr nonlinearity theoretically. We first construct the two-qubit KLM state, through which the three- and other n-qubit KLM states are generated. For the schemes using weak cross-Kerr nonlinearity, P homodyne measurement has a higher success rate than X homodyne measurement but with narrow applications since |αeiθ⟩ and |αe−iθ⟩ are distinguished from each other, which is undesirable for most of the entanglement generation schemes. To avoid this disadvantage, Jin et al. [Phys. Rev. A75, 054302 (2007)PLRAAN1050-294710.1103/PhysRevA.75.054302] introduced the coherent state superposition (CSS), c(|α⟩+|−α⟩), to generate a Greenberger-Horne-Zeilinger state but with a rapid oscillation term, which needs to be ignored. Through designing the optical path uniquely and choosing the phase of cross-Kerr nonlinearity suitably, our P homodyne measurement and CSS probe mode-based schemes to generate the KLM state avoid the needless term. The present scalable schemes have high total success probabilities, high fidelities even in consideration of decoherence, and may find potential applications in the future with the further development of nonlinear optics.
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.
The decoherence-free subspace (DFS) serves as a protective shield against certain types of environmental noise, allowing the system to remain coherent for extended periods of time. In this paper, we propose two protocols, i.e., one converts two-logic-qubit Knill-Laflamme-Milburn (KLM) state to two-logic-qubit Bell states, and the other converts three-logic-qubit KLM state to three-logic-qubit Greenberger-Horne-Zeilinger states, through cavity-assisted interaction in DFS. Especially, our innovative protocols achieve their objectives in a heralded way, thus enhancing experimental accessibility. Moreover, single photon detectors are incorporated into the setup, which can predict potential failures and ensure seamless interaction between the nitrogen-vacancy center and photons. Rigorous analyses and evaluations of two schemes demonstrate their abilities to achieve near-unit fidelities in principle and exceptional efficiencies. Further, our protocols offer progressive solutions to the challenges posed by decoherence, providing a pathway towards practical quantum technologies.