Quantum parameter estimation and coherent control with a time-dependent Hamiltonian

Dong Xie, Chunling Xu

We investigate simultaneous estimation of multi-parameter with time-dependent Hamiltonians. We analytically obtain the maximum quantum Fisher information matrix for two-parameter encoded in time-dependent three-level systems. The optimal coherent control scheme is proposed to increase the simultaneous multi-parameter estimation precisions. In an example of a spin-1 particle in a uniformly rotating magnetic field, the optimal coherent Hamiltonians for different parameters can be chosen to be completely same. However, in general, the optimal coherent Hamiltonians for different parameters are incompatible. In this situation, we suggest a variance method to obtain the optimal coherent Hamiltonian for simultaneously estimating multiple parameters, and obtain the optimal simultaneous estimation precision of two-parameter in a three-level Landau-Zener Hamiltonian.

M. R. James, Robert L. Kosut

Warren S. Warren

Mahdi Naghiloo, Andrew N. Jordan, K. W. Murch

Precision measurements of frequency are critical to accurate time keeping and are fundamentally limited by quantum measurement uncertainties. While for time-independent quantum Hamiltonians the uncertainty of any parameter scales at best as 1/T, where T is the duration of the experiment, recent theoretical works have predicted that explicitly time-dependent Hamiltonians can yield a 1/T^{2} scaling of the uncertainty for an oscillation frequency. This quantum acceleration in precision requires coherent control, which is generally adaptive. We experimentally realize this quantum improvement in frequency sensitivity with superconducting circuits, using a single transmon qubit. With optimal control pulses, the theoretically ideal frequency precision scaling is reached for times shorter than the decoherence time. This result demonstrates a fundamental quantum advantage for frequency estimation.

Robert Alicki

Jing Yang, Shengshi Pang, Andrew N. Jordan

We investigate the fundamental limits in precision allowed by quantum mechanics from Landau-Zener transitions, concerning Hamiltonian parameters. While the Landau-Zener transition probabilities depend sensitively on the system parameters, much more precision may be obtained using the acquired phase, quantified by the quantum Fisher information. This information scales with a power of the elapsed time for the quantum case, whereas it is time independent if the transition probabilities alone are used. We add coherent control to the system and increase the permitted maximum precision in this time-dependent quantum system. The case of multiple passes before measurement, Landau-Zener-Stueckelberg interferometry, is considered, and we demonstrate that proper quantum control can cause the quantum Fisher information about the oscillation frequency to scale as ${T}^{4}$, where $T$ is the elapsed time. These results are foundational for frequency standards and quantum clocks.