论文标题
希尔伯特·史克米特（Hilbert-Schmidt）速度是量子计量学的有效工具
Hilbert-Schmidt speed as an efficient tool in quantum metrology
论文作者
论文摘要
我们研究了Hilbert-Schmidt速度（HSS）是一种特殊类型的量子统计速度，可以用作一种功能强大且易于计算的工具，用于在$ n $ qubit System中进行量子相估计。我们发现，当HSS和量子Fisher信息（QFI）都相对于编码到$ n $ qubit寄存器的初始状态的相位参数计算时，HSS动力学的零与QFI动力学的零相同。此外，HSS的时间衍生的阳性（负（负）与QFI的时间衍生的阳性（消极）完全一致。如前所述，我们的结果还为HSS在完全正面和痕量保存图中的高维系统中的地图下的合同提供了有力的证据。
We investigate how the Hilbert-Schmidt speed (HSS), a special type of quantum statistical speed, can be exploited as a powerful and easily computable tool for quantum phase estimation in a $n$-qubit system. We find that, when both the HSS and quantum Fisher information (QFI) are computed with respect to the phase parameter encoded into the initial state of the $n$-qubit register, the zeros of the HSS dynamics are essentially the same as those of the QFI dynamics. Moreover, the positivity (negativity) of the time-derivative of the HSS exactly coincides with the positivity (negativity) of the time-derivative of the QFI. Our results also provide strong evidence for contractivity of the HSS under completely positive and trace preserving maps in high-dimensional systems, as predicted in previous studies.
