Non-destructive heralded entanglement with photons is a valuable resource for quantum information processing. However, they generally entail ancillary particles and modes that amplify the circuit intricacy. To address this challenge, a recent work [16] introduced a graph approach for creating multipartite entanglements with boson subtractions. Nonetheless, it remains an essential intermediate step toward practical heralded schemes: the proposition of heralded subtraction operators in bosonic linear quantum networks. This research establishes comprehensive translation rules from subtraction operators to linear optical operators, which provides a seamless path to design heralded schemes with single photons. Our method begets enhanced or previously unreported schemes for the $N$-partite GHZ state with $2N$ photons, $N$-partite W state with $2N+1$ photons and superposition of $N=3$ GHZ and W states with 9 photons. Our streamlined approach can straightforwardly design heralded schemes for multipartite entangled states by assembling the operators according to the guidence of sculpting bigraphs, hence significantly simplifies the quantum circuit design process.

中文翻译：

---

通过线性量子网络的图形图片预示着光纠缠的产生


与光子的非破坏性预示纠缠是量子信息处理的宝贵资源。然而，它们通常包含辅助粒子和模式，这些粒子和模式会放大电路的复杂性。为了应对这一挑战，最近的一项工作 [16] 引入了一种图方法，用于创建带有玻色子减法的多方纠缠。尽管如此，它仍然是迈向实际预示方案的重要中间步骤：玻色子线性量子网络中预示减法算子的命题。这项研究建立了从减法算子到线性光学算子的全面转换规则，这为设计具有单光子的预示方案提供了一条无缝的途径。我们的方法为具有 $2N$ 个光子的 $N$-partite GHZ 状态、具有 $2N+1$ 个光子的 $N$-partite W 状态以及具有 9 个光子的 $N=3$ GHZ 和 W 态的叠加产生了增强或以前未报道的方案。我们的简化方法可以根据雕刻双符的指导组装算子，从而直接为多方纠缠态设计预示方案，从而大大简化了量子电路设计过程。