Cabedo-Olaya Marina, Muga Juan Gonzalo, Martínez-Garaot Sofía
Departamento de Química Física, UPV/EHU, Apdo 644, 48080 Bilbao, Spain.
Entropy (Basel). 2020 Nov 3;22(11):1251. doi: 10.3390/e22111251.
Quantum metrology makes use of quantum mechanics to improve precision measurements and measurement sensitivities. It is usually formulated for time-independent Hamiltonians, but time-dependent Hamiltonians may offer advantages, such as a T4 time dependence of the Fisher information which cannot be reached with a time-independent Hamiltonian. In (Nature Communications 8, 2017), Shengshi Pang and Andrew N. Jordan put forward a Shortcut-to-adiabaticity (STA)-like method, specifically an approach formally similar to the "counterdiabatic approach", adding a control term to the original Hamiltonian to reach the upper bound of the Fisher information. We revisit this work from the point of view of STA to set the relations and differences between STA-like methods in metrology and ordinary STA. This analysis paves the way for the application of other STA-like techniques in parameter estimation. In particular we explore the use of physical unitary transformations to propose alternative time-dependent Hamiltonians which may be easier to implement in the laboratory.
量子计量学利用量子力学来提高精密测量和测量灵敏度。它通常是针对与时间无关的哈密顿量来表述的，但含时哈密顿量可能具有优势，比如费舍尔信息的T4时间依赖性，这是与时间无关的哈密顿量无法实现的。在2017年的《自然·通讯》第8期上，庞盛时和安德鲁·N·乔丹提出了一种类似绝热捷径（STA）的方法，具体是一种形式上类似于“反绝热方法”的途径，即在原始哈密顿量中添加一个控制项以达到费舍尔信息的上限。我们从STA的角度重新审视这项工作，以确定计量学中类似STA的方法与普通STA之间的关系和差异。这一分析为其他类似STA的技术在参数估计中的应用铺平了道路。特别是，我们探索利用物理幺正变换来提出替代的含时哈密顿量，这些哈密顿量可能在实验室中更易于实现。
