Quantum metrology, criticality, and classical brachistochrone problem
- URL: http://arxiv.org/abs/2303.10655v2
- Date: Mon, 8 May 2023 03:13:42 GMT
- Title: Quantum metrology, criticality, and classical brachistochrone problem
- Authors: Rui Zhang, Zhucheng Zhang, Lei Shao, Yuyu Zhang, and Xiaoguang Wang
- Abstract summary: We show that the generator $mathcalH$ in the unitary parametrization process can be treated as an extended brachistochrone problem.
In addition, we find that the value of quantum Fisher information is proportional to the sixth power of the evolution time when the system is close to the phase transition point.
- Score: 13.114256757378884
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: There has always been an ambiguous connection between quantum metrology and
criticality. We clarify this relationship in a unitary parametrization process
with a Hamiltonian governed by su(1,1) Lie algebra. Based on this type of
Hamiltonian, we investigate the quantum Cram\'{e}r-Rao bound of the coupling
strength in the quantum Rabi model close to the phase transition point. We show
that the generator $\mathcal{H}$ in the unitary parametrization process can be
treated as an extended brachistochrone problem on the $x-y$ plane and a linear
function of time in the $z$ direction. In addition, we find that the value of
quantum Fisher information is proportional to the sixth power of the evolution
time when the system is close to the phase transition point.
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