发表机构
Tel Aviv University（特拉维夫大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究未来参考反馈回路的量子寿命，证明相互作用轴上的有限纠缠破坏指标，并发现热浴轴上的架构下限与热增益，提供精确闭式解和广泛数值验证。
AI 中文摘要
一个量子反馈回路将前向模拟的信息返回到更早的内部时间，从而在消息寄存器上诱导一个完全正迹保持映射；迭代该映射最终会破坏其携带纠缠的能力。纠缠破坏指标 N = n_EB(Phi)，即发生这一现象的轮次，本文沿两条轴线进行研究：相互作用轴和热浴轴。在相互作用轴上，我们证明严格收缩到满秩不动点迫使 N 在任意维度下有限，通过围绕极限 Choi 态的显式可分离球实现；对于各向同性幺正信道，量子比特闭式解超过精确答案的因子为 ln(2 sqrt 3) / ln 3 = 1.1309...，并且在 3997 个采样信道上，指标与稳定性间隙相差一个时钟，N [1 - rho(A)] 位于 [0.60, 1.50] 区间。在热浴轴上，将零温辅助体替换为极化 p = tanh(hbar omega / 2 k_B T) 的热辅助体，使得每个信道量成为 p 的精确二次多项式，并且相同的一侧认证（无需特征值求解器）在参考电路上于任意温度下确立 N = 3，且在参数盒上一致成立。无限温度指标是一个架构下限，具有闭式解和精确度量（46.427% 的电路在一轮内破坏纠缠，无论热浴多热）。该下限并非界限：认证电路在内部温度窗口中低于该下限，深度按单位量子化；在超过 410 万个电路上，其比率遵循 epsilon = 1 - ||A||_2 的高斯截断，指数为 2.02 [1.90, 2.16]，另有 1200 万个认证电路显示谷值存活至 epsilon = 0.125。认证端点使比较精确：温度最多将指标移动 21/14 = 3/2；相互作用将其移动 1213/3。
英文摘要
A quantum feedback loop that returns information from a forward simulation to an earlier internal time induces a completely positive trace-preserving map on a message register; iterating that map eventually destroys its ability to carry entanglement. The entanglement-breaking index N = n_EB(Phi), the round at which this happens, is studied here along two axes: the interaction and the bath. On the interaction axis we prove that strict contraction onto a full-rank fixed point forces N finite in every dimension, via an explicit separable ball around the limiting Choi state; the qubit closed form overshoots the exact answer by the factor ln(2 sqrt 3) / ln 3 = 1.1309... on isotropic unital channels, and across 3997 sampled channels index and stability gap are one clock, N [1 - rho(A)] in [0.60, 1.50]. On the bath axis, replacing the zero-temperature ancilla by a thermal one at polarisation p = tanh(hbar omega / 2 k_B T) makes every channel quantity an exact quadratic polynomial in p, and the same one-sided certificates (no eigensolver) establish N = 3 at the reference circuit at every temperature, uniformly on a parameter box. The infinite-temperature index is an architecture floor with closed form and exact measure (46.427% of circuits break entanglement in one round however hot the bath). The floor is not a bound: certified circuits dip below it in interior temperature windows, unit-quantised in depth; over 4.1 million circuits their rate follows a Gaussian cutoff in epsilon = 1 - ||A||_2 with exponent 2.02 [1.90, 2.16], and 12 million more certified circuits show valleys surviving to epsilon = 0.125. Certified endpoints make comparisons exact: temperature moves the index by at most 21/14 = 3/2; the interaction moves it by 1213/3.
Comments33 pages, 1 figure, 9 tables. Companion to arXiv:2608.13764. Ancillary files in two subfolders: zero-temperature/ and thermal/
