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

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