AI 中文总结
本研究针对引力红移下受两种噪声信道影响的光子系统，通过计算Holevo Cramer-Rao界和Nagaoka界等，分析多参数量子估计的误差界及不同参数区域的估计精度。
AI 中文摘要
当光子在弯曲时空中传播时，引力效应不可避免。特别地，引力红移会导致光子波包产生显著畸变，因此在该背景下研究参数估计至关重要。此前研究多聚焦于利用量子Cramer-Rao界的单参数估计，而多参数场景在很大程度上仍未被探索。本工作研究受引力红移影响的光子系统在振幅阻尼和类欧姆退相位两种信道下的多参数量子估计。分析表明，量子Cramer-Rao界无法为涉及初始相位和权重参数的两参数估计提供紧误差界。为克服此局限，我们利用半定规划数值计算两种更紧的误差界，即Holevo Cramer-Rao界和Nagaoka界，结果显示Nagaoka界在所有考虑的界中给出最紧的误差界，与多参数量子估计的一般层级一致。此外，对于包含初始权重参数、相位参数和引力红移强度的三参数估计，在振幅阻尼信道下，强耦合区域的估计精度显著高于弱耦合区域；类似地，在类欧姆退相位信道下，亚欧姆区域的估计精度始终高于欧姆和超欧姆区域。
英文摘要
As photons propagate through curved spacetime, gravitational effects become unavoidable. In particular, gravitational redshift can induce significant distortion in photon wave packets, making it es?sential to investigate parameter estimation within this context. While previous research has focused on single-parameter estimation using the quantum Cramer-Rao bound, the multiparameter scenario remains largely unexplored. In this work, we investigate multiparameter quantum estimation for a photon system subject to gravitational redshift under both amplitude-damping and Ohmic-like dephasing channels. Our analysis reveals that the quantum Cramer-Rao bound fails to provide a tight error bound for the two-parameter estimation involving the initial phase and weight parameters inboth types of noisy channels. To overcome this limitation, we numerically compute two tighter error bounds, i.e., the Holevo Cramer-Rao bound and the Nagaoka bound, when utilizing a semidefinite program. We demonstrate that the Nagaoka bound yields the tightest error bound among all considered bounds, consistent with the general hierarchy of multiparameter quantum estimation. Furthermore, for the three-parameter estimation, including the initial weight parameter, the phase parameter, and the strength of gravitational redshift, we observe significantly enhanced estimation precision in the strong-coupling regime compared to the weak-coupling regime under the amplitude-damping channel. Similarly, in the Ohmic-like dephasing channel, the sub-Ohmic regime consistently affords higher precision than the Ohmic and super-Ohmic regimes.
