Abstract
Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case.
Highlights
Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians
While there has been tremendous research devoted to quantum metrology, most of those works were focused on timeindependent Hamiltonians, and little has been known when the Hamiltonians are varying with time. (The most relevant work so far to our knowledge includes ref. that uses basis splines to approximate a time-dependent Hamiltonian of a qubit, and ref. that studies the quantum Cramer–Rao bound for a timevarying signal and so on) in reality, many factors that influence the systems are changing with time, for example, periodic driving fields or fluctuating external noise
Based on the general results obtained, we surprisingly find that some fundamental limits in quantum metrology with time-independent Hamiltonians can be broken with time-dependent Hamiltonians
Summary
Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T4 in estimating the rotation frequency of the field. Quantum mechanics opens new possibilities for improving measurement sensitivities by utilizing non-classical resources, such as quantum entanglement and squeezing[2] These have given rise to the wide interest in quantum parameter estimation[3,4] and quantum metrology[5,6]. In a minimal example of a qubit in a rotating magnetic field, we show that the time-scaling of Fisher information for the rotation frequency of the field can reach T4 in the presence of the optimal Hamiltonian control, significantly exceeding the traditional limit
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