AI 中文总结
研究全连接三模压缩真空态，利用有序积内积分技术推导相关形式与矩阵。分析其纠缠、导引特性及光子减法情况，区分成对和集体非经典资源，阐明完全图拓扑操作作用，如对称耦合下的纠缠见证、导引特性及光子减法的不同结果。
AI 中文摘要
我们研究了全连接三模压缩真空（FC-C3MSV）态，其中所有三个模式通过三角形（$K_3$）拓扑中的非线性相互作用成对耦合。利用有序积内积分技术，我们推导了压缩算符的正规积形式，并直接从博戈留波夫变换获得协方差矩阵。在对称耦合下，对于任何非零压缩，物理态是真正的三方纠缠，而三个阿姆斯特朗型见证者提供了有限窗口的充分实验测试；在链型C3MSV中，只有一个这样的见证者被违反。我们发现，尽管存在双模纠缠，但全连接拓扑在任何一对物理模式之间都不存在双模高斯导引（$\mathcal{G}^{i\to j}=0$）；相反，导引资源是集体的单模对双模导引$\mathcal{G}^{i\to jk}$，它与$\theta$无关且随$r$增长。我们分析了独立的真空损耗并获得了导引存活的临界透过率：在$r = 0.5$时的全对称损耗下，一对二集体导引在$\eta\approx0.58$时消失，而反向的二对一集体导引在$\eta\approx0.502$时仍存在，并且潜在的双模纠缠在所有$\eta>0$时都持续存在。最后，我们使用归一化相空间推导重新审视光子减法。在单个物理模式上进行光子减法不会在另一个单模上产生维格纳负性，这与不存在双模导引一致。相反，当鲍勃从集体模式$(b + c)/\sqrt{2}$中减去光子时，可以产生维格纳负性，在$r = 0.5$时损耗阈值$\eta_c\approx0.667$。这些结果区分了FC-C3MSV中的成对和集体非经典资源，并阐明了完全图拓扑的操作作用。
英文摘要
We investigate a fully-connected three-mode squeezed vacuum (FC-C3MSV) state, where all three modes are pairwise coupled through nonlinear interactions in a triangle ($K_3$) topology. Using the integration-within-ordered-product technique, we derive the normal product form of the squeezing operator and obtain the covariance matrix directly from the Bogoliubov transformation. Under symmetric coupling, the physical state is genuinely tripartite entangled for any nonzero squeezing, while the three Armstrong-type witnesses provide a finite-window sufficient experimental test; in the chain-type C3MSV only one of these witnesses is violated. We find that, despite two-mode entanglement, the fully-connected topology admits \emph{no} two-mode Gaussian steering ($\mathcal{G}^{i\to j}=0$) between any pair of physical modes; the steering resource is instead collective one-mode-versus-two steering $\mathcal{G}^{i\to jk}$, which is $θ$-independent and grows with $r$. We analyze independent vacuum losses and obtain critical transmittances for steering survival: under full symmetric loss at $r=0.5$, one-to-two collective steering disappears at $η\approx0.58$, whereas reverse two-to-one collective steering survives down to $η\approx0.502$ and the underlying two-mode entanglement persists for all $η>0$. Finally, we revisit photon subtraction using a normalized phase-space derivation. A photon subtraction on a single physical mode does not generate Wigner negativity on another single mode, consistent with the absence of two-mode steering. Wigner negativity can instead be generated when Bob subtracts from the collective mode $(b+c)/\sqrt{2}$, with a loss threshold $η_c\approx0.667$ at $r=0.5$. These results distinguish pairwise and collective nonclassical resources in the FC-C3MSV and clarify the operational role of the complete-graph topology.
Comments15 pages, 5 figures
