We present a semianalytical methodology to construct optimal linear-optical circuits for the heralded production of three-photon Greenberger-Horne-Zeilinger (3-GHZ) and two-photon Bell states. We provide a detailed description and analysis of the resulting optical schemes, which deliver success probabilities of 1/54 and 2/27 for dual-rail encoded 3-GHZ and Bell-state generation, respectively. Our results improve the known constructive bounds on the success probabilities for 3-GHZ states and are of particular importance for a ballistic quantum computing model [M. Gimeno-Segovia et al., Phys. Rev. Lett. 115, 020502 (2015)], for which these states provide an essential resource.

中文翻译：

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改进的预示方案可从单光子生成纠缠态

我们提出了一种半解析方法，以构造用于三光子格林伯格-霍尔恩-泽林格（3-GHZ）和两光子贝尔状态的先驱生产的最佳线性光学电路。我们对所得的光学方案进行了详细的描述和分析，对于双轨编码的3-GHZ和贝尔状态产生，它们分别提供了成功概率1/54和2/27。我们的结果改善了3-GHZ状态成功概率的已知构造性边界，对于弹道量子计算模型[M. Gimeno-Segovia等。，物理 牧师 115，020502（2015）]，为此，这些状态提供的基本资源。