AI 中文总结
该研究分析后栅噪声对CNOT门产生的相位编码X态的纠缠与相位信息的不同影响，发现存在可分但仍具相位敏感性的态区域，给出残余QFI并对比测量方案，为相位信息保留提供参考基准。
AI 中文摘要
理想的CNOT门将相干量子比特的相位映射到两量子比特态的|00⟩和|11⟩之间的相干性上，产生的输出同时携带纠缠和可估计的相位信息。我们研究后栅噪声如何降低这两个量，发现它们不会同时消失。对于该协议产生的相位编码X态，负性（negativity）是幸存相干性z=fκ与布居数惩罚g的阈值差，当fκ≤g时消失；而相位量子费舍尔信息（QFI）是平滑比值F_φ=4z²/(a+b)，在任何非零相干性下均保持正值。因此，存在一个精确的态空间区域，其中输出是可分的，但仍具有相位敏感性。我们表征了该区域，给出纠缠死亡时的残余QFI F_φ^★=4g_★²/(1-2g_★)，并证明在相同坐标下达到死亡的通道共享该残余量，全局和独立的局域去极化是这类通道之一，在最大输入相干性下F_φ^★=1/6。四个标准通道作为该共同几何中的轨迹出现，非对称布居数转移增加了第三个坐标，改变纠缠但不改变QFI，这标志着两坐标描述的适用范围。我们确定了达到该界限的测量，并与直接单量子比特探针进行比较，后者在匹配曝光下更精确；因此，这些结果是相位信息保留的参考基准，而非计量学优势的主张。
英文摘要
An ideal CNOT maps the phase of a coherent qubit onto the coherence between $\ket{00}$ and $\ket{11}$ of a two-qubit state, producing an output that carries both entanglement and estimable phase information. We ask how post-gate noise degrades these two quantities, and find that they are not lost together. For the phase-encoded X states generated by the protocol, the negativity is a thresholded difference of the surviving coherence $z=fκ$ and a population penalty $g$, vanishing once $fκ\le g$, while the phase quantum Fisher information (QFI) is the smooth ratio $F_ϕ=4z^2/(a+b)$, which stays positive for any nonzero coherence. As a result there is an exact region of state space in which the output is separable but still phase-sensitive. We characterize this region, give the residual QFI $F_ϕ^\star=4g_\star^2/(1-2g_\star)$ at entanglement death, and show that channels reaching death at the same coordinate share this residual, with global and independent local depolarization forming one such class and $F_ϕ^\star=1/6$ at maximal input coherence. Four standard channels appear as trajectories through this common geometry, and asymmetric population transfer adds a third coordinate that changes the entanglement but leaves the QFI unchanged, which marks where the two-coordinate description applies. We identify a measurement that attains the bound and compare with a direct single-qubit probe, which is more precise under matched exposure; the results are therefore reference benchmarks for phase-information retention, not a claim of metrological advantage.
