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Optics Express

Error-protected photonic logical cluster states generation based on photonic Faraday rotation in an atom-cavity coupling system

Li Dong, Xin-Yi Zhang, Xin‐Ying Wang, Si-Ge Chen, Ming Cong, Shi-Yi Li, Fei-Yu Su, Yuan‐Peng Ren, Yan‐Qiang Ji, Xiao‐Ming Xiu

Published May 13, 2026• 0 citations
Publisher

Abstract

Logical entangled states are essential for quantum information processing due to their robustness against environmental noise and decoherence. We propose a scheme for generating logical cluster states based on photonic Faraday rotation in atom-cavity coupling systems. A physical cluster state is generated first. Subsequently, additional single photons assist in transforming each physical qubit into a physical GHZ state, which serves as a logical qubit. After replacing all physical qubits with logical qubits, the logical cluster state is obtained. The responses of photon detectors reveal low-probability errors arising from photon input-output imbalances, but these measurements do not induce scheme failure. Optical attenuators balance optical paths, guaranteeing unity fidelity in theory.

DOI
10.1364/oe.587623

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Logical entangled states are essential for quantum information processing due to their robustness against environmental noise and decoherence. We propose a scheme for generating logical cluster states based on photonic Faraday rotation in atom-cavity coupling systems. A physical cluster state is generated first. Subsequently, additional single photons assist in transforming each physical qubit into a physical GHZ state, which serves as a logical qubit. After replacing all physical qubits with logical qubits, the logical cluster state is obtained. The responses of photon detectors reveal low-probability errors arising from photon input-output imbalances, but these measurements do not induce scheme failure. Optical attenuators balance optical paths, guaranteeing unity fidelity in theory.
Abstract The central technological appeal of quantum science resides in exploiting quantum effects, such as entanglement, for a variety of applications, including computing, communication and sensing 1 . The overarching challenge in these fields is to address, control and protect systems of many qubits against decoherence 2 . Against this backdrop, optical photons, naturally robust and easy to manipulate, represent ideal qubit carriers. However, the most successful technique so far for creating photonic entanglement 3 is inherently probabilistic and, therefore, subject to severe scalability limitations. Here we report the implementation of a deterministic protocol 4–6 for the creation of photonic entanglement with a single memory atom in a cavity 7 . We interleave controlled single-photon emissions with tailored atomic qubit rotations to efficiently grow Greenberger–Horne–Zeilinger (GHZ) states 8 of up to 14 photons and linear cluster states 9 of up to 12 photons with a fidelity lower bounded by 76(6)% and 56(4)%, respectively. Thanks to a source-to-detection efficiency of 43.18(7)% per photon, we measure these large states about once every minute, which is orders of magnitude faster than in any previous experiment 3,10–13 . In the future, this rate could be increased even further, the scheme could be extended to two atoms in a cavity 14,15 or several sources could be quantum mechanically coupled 16 , to generate higher-dimensional cluster states 17 . Overcoming the limitations encountered by probabilistic schemes for photonic entanglement generation, our results may offer a way towards scalable measurement-based quantum computation 18,19 and communication 20,21 .
We propose a scheme to implement a two-qubit controlled-phase gate for single atomic qubits, which works in principle with nearly ideal success probability and fidelity. Our scheme is based on the cavity input-output process and the single-photon polarization measurement. We show that, even with the practical imperfections such as atomic spontaneous emission, weak atom-cavity coupling, violation of the Lamb-Dicke condition, cavity photon loss, and detection inefficiency, the proposed gate is feasible for generation of a cluster state in that it meets the scalability criterion and it operates in a conclusive manner. We demonstrate a simple and efficient process to generate a cluster state with our high probabilistic entangling gate.
Based on the input-output relation in low-Q cavities, we propose a feasible scheme to prepare remotely a single-atom state via photonic Faraday rotation, and then the scheme is generalized to the case of remote preparation of a two-atom entangled state. Our results show that when the coefficients of the initial atomic state to be prepared are real, both remote preparation of the single-atom state and that of the two-atom entangled state can be achieved deterministically by selecting appropriate parameters of the systems for the interactions among the atom, polarized single-photon pulse, and cavity field. Compared with the existing schemes for remote preparation of atomic states, in our scheme photons are used as flying qubits to transmit quantum information, which is suitable indeed to achieve a long-distance atomic state preparation in principle. Due to the fact that the information of atomic state is encoded in two degenerate ground-state levels of a -type three-level atom confined in a unilateral dissipative cavity, and that the atoms are only virtually excited, our schemes are insensitive to both cavity decay and atomic spontaneous emission. Besides, the two schemes we proposed do not need two- or multi-particle orthogonal measurements, only product-state measurements are involved, as well as they work in low-Q regime and do not require a strong coupling condition between the atoms and the optical cavities, which greatly reduce the experimental difficulty.
We propose a scheme to prepare the GHZ state of the atoms using the Faraday rotation produced by the input and output process of photons in the low quality cavity.The coupling between atom and cavity isn't strong in the scheme.Meanwhile,the quantum information is encoded in the low energy level of atoms.Therefore,our scheme is insensitive to both cavity decay and atomic spontaneous emission.In addition,we need not to impose the classical field or choose interaction time during the whole process,which reduces the difficulty of experiment.
The logic Bell-state which encodes many physical qubits in a logic qubit has great application potential in the future quantum communication field, for it is robust to the decoherence in a noisy environment. In this paper, we propose a complete logic Bell-state analysis (LBSA) with the help of the auxiliary single atoms trapped in the low-quality cavity. We construct the parity-check measurement gate based on the photonic Faraday rotation effect and complete the task combined with the Hadamard operation and single-qubit measurement. The number of physical qubits encoded in each logic qubit does not affect the analysis. We also discuss the application of this LBSA in the fields of quantum teleportation and logic-qubit entanglement swapping. Our LBSA protocol may have practical application in future long-distance quantum communication.