Southwest Quantum Information and Technology

Optimal control for quantum metrology with time-dependent Hamiltonians

Presenting Author: Shengshi Pang, University of Rochester
Contributing Author(s): Andrew N. Jordan

Due to its importance in many areas of physics, quantum metrology has attracted a growing attention in recent years. Most of the current researches on quantum metrology were focused on systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, little has been known due to the complexity of dynamics. In this work, we study quantum metrology with general time-dependent Hamiltonians to bridge this gap. We obtain the maximum quantum Fisher information for general parameters in time-dependent Hamiltonians, and find that proper Hamiltonian control on the system is necessary to reach the maximum Fisher information. We derive the optimal Hamiltonian control in general, and show that it is generally an adaptive and feedback-based control. With a minimal example of a qubit in a rotating magnetic field, we surprisingly find that the time scaling of quantum Fisher information reaches T^4 in estimating the rotation frequency of the field, which significantly breaks the traditional limit of T^2 time scaling for quantum Fisher information with time-independent Hamiltonians. This suggests a dramatic difference between quantum metrology with time-dependent Hamiltonians and time-independent Hamiltonians, and also shows the advantage of quantum control in enhancing quantum metrology. We conclude by considering the effect of level crossings in the derivative of the Hamiltonian with respect to the parameter of interest, and point out that additional control on the Hamiltonian is necessary for that case.

Read this article online: https://arxiv.org/abs/1606.02166

(Session 5 : Thursday from 5:00pm - 7:00pm)