在数值精度范围内达到关于去极化SU(2)旋转信道的贝叶斯长冈 - 林界限
Saturating the Bayesian Nagaoka-Hayashi bound within numerical precision for the depolarization SU(2) rotation channel
AI总结：
研究在去极化噪声和均匀先验下，通过k次并行使用信道一次性估计量子比特旋转所有参数的问题，利用旋转协方差简化优化，发现优化策略在数值精度内达到NH界限，证明该信道族能达到此界限，而SLD界限未达。
AI中文摘要：
贝叶斯长冈 - 林（NH）界限是多参数估计贝叶斯风险的半定下界，比贝叶斯对称对数导数（SLD）克拉美 - 罗界限更紧，其能否达到是个开放问题。我们研究在去极化噪声和均匀先验下，通过k次并行使用信道一次性估计量子比特旋转的所有三个参数。旋转协方差将探测器、测量和估计器的联合优化以及NH界限本身简化为小型半定规划，通过k = 4可解。在每种使用次数和噪声强度下，优化策略在计算的数值精度内达到NH界限，表明该信道族能达到此界限，而SLD界限严格低于且从未达到。随着噪声增加，最优探测器坍缩为张量积贝尔态。
英文摘要：
The Bayesian Nagaoka--Hayashi (NH) bound is a semidefinite lower bound on the Bayes risk of multiparameter estimation, tighter than the Bayesian symmertic logarithmic derivative (SLD) Cramér--Rao bounds, and whether it can be attained is an open problem. We study the single-shot estimation of a qubit rotation, all three parameters at once, under depolarizing noise and a uniform prior, with $k$ parallel uses of the channel. Rotational covariance reduces the joint optimization of probe, measurement, and estimator, and the NH bound itself, to small semidefinite programs, solvable through $k=4$. At every number of uses and noise strength the optimized strategy reaches the NH bound within the numerical precision of the calculation, numerical evidence that the bound is attained for this channel family, while the SLD bound lies strictly below and is never attained. As the noise grows the optimal probe collapses to the tensored Bell state.
