Super-Heisenberg scaling in Hamiltonian parameter estimation in the long-range Kitaev chain

TL;DR

This paper demonstrates that in long-range Kitaev chains, the quantum Fisher information can surpass Heisenberg scaling, achieving super-Heisenberg precision through interaction range tuning and quantum control.

Contribution

It establishes a transition from Heisenberg to super-Heisenberg scaling in long-range systems and shows quantum control can enhance quantum metrology performance.

Findings

Quantum Fisher information exhibits super-Heisenberg scaling with interaction range.

Quantum control improves the prefactor of quantum Fisher information.

Long-range interactions provide an advantage in many-body quantum metrology.

Abstract

In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass the Heisenberg scaling. Here, we consider the estimation of the interaction strength in linear systems with long-range interactions and using the Kitaev chains as a case study, we establish a transition from the Heisenberg to super-Heisenberg scaling in the quantum Fisher information by varying the interaction range. We further show that quantum control can improve the prefactor of the quantum Fisher information. Our results explore the advantage of optimal quantum control and long-range interactions in many-body quantum metrology.