Relations between quantum metrology and criticality in general su(1, 1) systems

Abstract

There is a prevalent effort to achieve quantum-enhanced metrology using criticality. However, the extent to which estimation precision is enhanced through criticality still needs further exploration under the constraint of finite time resources. We clarify relations between quantum metrology and criticality through a unitary parametrization process with a Hamiltonian governed by su(1, 1) Lie algebra. We demonstrate that the determination of the generator in the parameterization can be treated as an extended brachistochrone problem. Furthermore, the dynamic quantum Fisher information about the parameter exhibits a power-law dependence on the evolution time as the system approaches its critical point. By investigating the dynamic sensing proposals of three quantum critical systems, we show that the asymptotic behavior of sensitivity is consistent with our predictions. Our theory provides a deep understanding on the interplay of quantum metrology and criticality, providing insights into the underlying connections that involve both quantum phenomena and classical problems.