时变通道中的量子隐形传态：阈值几何与非马尔可夫回流的完全正定性界
Teleportation through time-varying channels: threshold geometry and a complete-positivity bound on non-Markovian backflow
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中文总结 AI 辅助
该研究分析时变噪声通道中Bell对隐形传态的特性，推导Horodecki保真度公式的适用条件，明确对称/单侧噪声下的纠缠行为，给出谐波调制速率下非马尔可夫回流的完全正定性界。
中文摘要 AI 辅助
一个Bell对通过结合振幅阻尼和时速率退相的链路进行分发，其动力学可分离为固定部分和移动部分。负性、完全纠缠分数、量子失谐以及平均隐形传态保真度仅通过累积阻尼参数p(t)和q(t)依赖于时间，因此每个阈值都是单位正方形内的一条固定曲线，而速率仅决定穿过该曲线的轨迹。Horodecki保真度公式$\bar{F} = \frac{1}{2} + \frac{1}{6}\text{Tr}|T|$适用于单侧和双侧暴露两种情况，两种情况在整个单位正方形内均满足该公式形式对应的条件$\text{det} T \blacktriangleleft 0$。在对称双侧噪声下，当$p+q\blacktriangleleft1$时纠缠消失，精确关系$\bar{F}^{2s}=\frac{2}{3}+\frac{1}{3}\text{N}_{2s}$将退纠缠与量子优势丧失关联到同一时刻。单侧暴露在任意速率分布下均无有限时间的纠缠突然死亡，且量子失谐在整个开正方形内严格为正，因此分发的态可分离、对隐形传态无用但仍非经典。对于谐波调制速率，完全正定性将回流限制在一个静态衰减的调制周期内，即$\triangle\blackGamma_{k}\blacktriangleleft2\boldsymbol{\text{π}}\blackgamma_{k,0}/\blackOmega$，等价于调制深度$\blackxi_{k}\blacktriangleleft4.6033$，且该值与$\blackOmega$无关。在该区间内轨迹反转，产生恢复量子优势和纠缠突然产生的有限区间。
英文摘要
A Bell pair distributed through a link that combines amplitude damping with dephasing at time-dependent rates has dynamics that separate into a fixed part and a moving one. The negativity, fully entangled fraction, discord, and average teleportation fidelity depend on time only through the accumulated damping parameters $p(t)$ and $q(t)$. Every threshold is therefore a curve fixed in the unit square, and the rates select nothing but a trajectory across it. The Horodecki fidelity formula $\bar{F} = \frac{1}{2} + \frac{1}{6}\mathrm{Tr}|T|$ covers one- and two-sided exposure alike: the condition $\det T \leq 0$ under which it takes this form holds throughout the unit square for both. Under symmetric two-sided noise the entanglement vanishes when $p+q\geq1$, where the exact relation $\bar{F}^{2s}=\frac{2}{3}+\frac{1}{3}\mathcal{N}_{2s}$ ties disentanglement and the loss of quantum advantage to the same instant. One-sided exposure admits no finite-time sudden death for any rate profile, and the discord stays strictly positive throughout the open square, so the distributed state can be separable, useless for teleportation, and still nonclassical. For harmonically modulated rates, complete positivity caps the backflow at one modulation period of static decay, $ΔΓ_{k}\leq2πγ_{k,0}/Ω$, equivalently at a modulation depth $ξ_{k}\leq4.6033$ independent of $Ω$. Inside that window the trajectory reverses, producing finite intervals of restored quantum advantage and entanglement sudden birth.
