Quantum metrology for a general Hamiltonian parameter

By Shengshi Pang, Todd A. Brun. 2014

132 citations recorded by the source corpus.

Quantum metrology enhances the sensitivity of parameter estimation using the distinctive resources of quantum mechanics such as entanglement. It has been shown that the precision of estimating an overall multiplicative factor of a Hamiltonian can be increased to exceed the classical limit, yet little is known about estimating a general Hamiltonian parameter. In this paper, we study this problem in detail. We find that the scaling of the estimation precision with the number of systems can always be optimized to the Heisenberg limit, while the time scaling can be quite different from that of estimating an overall multiplicative factor. We derive the generator of local parameter translation on the unitary evolution operator of the Hamiltonian, and use it to evaluate the estimation precision of the parameter and establish a general upper bound on the quantum Fisher information. The results indicate that the quantum Fisher information generally can be divided into two parts: one is quadratic in time, while the other oscillates with time. When the eigenvalues of the Hamiltonian do not depend on the parameter, the quadratic term vanishes, and the quantum Fisher information will be bounded in this case. To illustrate the results, we give an example of estimating a parameter of a magnetic field by measuring a spin-$\frac{1}{2}$ particle and compare the results for estimating the amplitude and the direction of the magnetic field.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/3c5fc3f1a377d708a0180ed4a174626003cdcaa2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum-enhanced measurements without entanglement (2017, background): “It was shown in (Pang and Brun, 2014, 2016) that in such a case the quantum Fisher information becomes periodic in time.”
Quantum Fisher information matrix and multiparameter estimation (2019, methodology): “The density matrix ρ x+dxa can then be approximately calculated as ρ x+dxa = e −iKadxaρeiKadxa [53], which indicates that Ka is the generator of U along parameter xa.”