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Annalen der Physik

Deterministic Kerr‐Effect‐Based Mutual Conversions of Entangled States in Decoherence‐Free Subspace

Fang‐Fang Du, Hao‐Lin Shi, Xue‐Shuo Deng, Cheng‐Yan Gao, Qiulin Tan

Published Aug 26, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1002/andp.202500319

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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.
Abstract The interconversion between different types of entangled states is an essential process. It is particularly important for tasks requiring specific forms of entanglement, as it greatly enhances the versatility, robustness, and efficiency of quantum systems. In the paper, deterministic schemes are proposed for interconversion between three‐logic‐qubit W state and three‐logic‐qubit Knill‐Laflamme‐Milburn state within a decoherence‐free subspace (DFS). The process of mutual transformation leverages the state‐selective nature of a quantum dot (QD) confined in a double‐sided microcavity, along with high‐fidelity, error‐predictable quantum control gates. Furthermore, the incorporation of single‐photon detectors helps to identify and mitigate potential failures arising from imperfect interactions between photons and the QD‐cavity system, thereby significantly enhancing experimental viability. In‐depth analyses of both protocols confirm that they can, in principle, achieve near‐unit fidelities and outstanding efficiencies. Additionally, the protocols offer advanced solutions to decoherence challenges through the use of DFS, paving the way for the development of practical quantum technologies.
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.
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.
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.
Abstract The interconversion of a variety of entangled states can facilitate the information transmission and decline the risk of error rates. Here two faithful protocols to achieve deterministic interconversion between three‐logic‐qubit W state and three‐logic‐qubit Greenberger–Horne–Zeilinger state in decoherence‐free subspace (DFS), resorting to the state‐selective property of the quantum dot (QD)‐cavity systems and robust‐fidelity quantum control gates are presented. Moreover, the single‐photon detectors introduced can effectively herald and mitigate potential failures from imperfect interaction between the QD‐cavity system and photons, significantly enhancing experimental feasibility. Through comprehensive analysis and evaluation, the protocols demonstrate exceptional conversion efficiencies and deliver near‐perfect fidelities. Additionally, the DFS makes system coherence over extended periods to overcome the decoherence effect caused by specific environmental noise, paving the way for quantum information processing.