Abstract
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 time dependence of the Fisher information which cannot be reached with a time-independent Hamiltonian. In Optimal adaptive control for quantum metrology with time-dependent Hamiltonians (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.
Highlights
Quantum metrology aims at high-resolution and highly sensitive measurements of parameters using advantages provided by quantum states and dynamics
Reaching the upper bound of the Fisher information may require Hamiltonian control [1], i.e., adding an extra term Hc (t) to the original Hamiltonian of the system Hg (t) to implement the necessary dynamics
(b) To get the upper bound of the Fisher information, in addition to following the state dynamics, the eigenvalues of ∂ g Htot should be the “right ones”, i.e., those of ∂ g Hg
Summary
Quantum metrology aims at high-resolution and highly sensitive measurements of parameters using advantages provided by quantum states and dynamics. The first term provides the right maximal and minimal eigenvalues of ∂ g Hg (t), ∂ g Htot (t) = ∂ g Hg (t), whereas the whole sum (≈ Hcd ( g) but not exactly) essentially drives the two corresponding eigenstates as dynamical solutions of the full Hamiltonian. This structure implies the need for an “adaptive scheme”, i.e., a guess value gc is taken as starting point to produce a better estimate gc0 and so on.
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