Yang Jing, Pang Shengshi, Chen Zekai, Jordan Andrew N, Del Campo Adolfo
Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg.
School of Physics, Sun Yat-Sen University, Guangzhou, Guangdong 510275, China.
Phys Rev Lett. 2022 Apr 22;128(16):160505. doi: 10.1103/PhysRevLett.128.160505.
We develop a variational principle to determine the quantum controls and initial state that optimizes the quantum Fisher information, the quantity characterizing the precision in quantum metrology. When the set of available controls is limited, the exact optimal initial state and the optimal controls are, in general, dependent on the probe time, a feature missing in the unrestricted case. Yet, for time-independent Hamiltonians with restricted controls, the problem can be approximately reduced to the unconstrained case via Floquet engineering. In particular, we find for magnetometry with a time-independent spin chain containing three-body interactions, even when the controls are restricted to one- and two-body interaction, that the Heisenberg scaling can still be approximately achieved. Our results open the door to investigate quantum metrology under a limited set of available controls, of relevance to many-body quantum metrology in realistic scenarios.
我们提出一种变分原理，以确定优化量子费舍尔信息的量子控制和初始状态，量子费舍尔信息是表征量子计量精度的量。当可用控制集有限时，精确的最优初始状态和最优控制通常取决于探测时间，这是无限制情况下所没有的特征。然而，对于具有受限控制的与时间无关的哈密顿量，通过弗洛凯工程，该问题可以近似简化为无约束情况。特别是，我们发现对于具有包含三体相互作用的与时间无关的自旋链的磁力测量，即使控制限于一体和两体相互作用，仍然可以近似实现海森堡标度。我们的结果为在有限的可用控制集下研究量子计量打开了大门，这与现实场景中的多体量子计量相关。
