Shortcut-to-adiabaticity-like techniques for parameter estimation in quantum metrology

TL;DR

This paper explores Shortcut-to-adiabaticity-like techniques in quantum metrology, comparing them to traditional STA and proposing alternative Hamiltonians for improved parameter estimation.

Contribution

It analyzes STA-like methods in quantum metrology, clarifies their relation to traditional STA, and proposes new Hamiltonians for experimental feasibility.

Findings

STA-like methods can reach Fisher information bounds

Alternative Hamiltonians may be easier to implement

Analysis clarifies differences between STA and STA-like approaches

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 $T^4$ 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.