Enhanced estimation of quantum evolution parameters with entangled states

Tao, Hong, Xiaoqing Tan

In the SU(2) dynamics, it is especially significant to achieve a simultaneous optimal multiparameter estimation but it is very difficult. Evolution on SU(N) dynamics is a research method to explore simultaneous multiparameter estimation with the quantum network. As the highly entangled states, graph state, is an intrinsical quantum resource for quantum metrology. For n-qubit graph state, we propose a simultaneous multiparameter estimation scheme that investigates evolution in SU(N) dynamics. For single-parameter estimation, the precision limit beyond the Heisenberg limit in the higher dimension spin of SU(2). We consider two scenarios where the Hamiltonian operator is commutation and non-commutation respectively and verify that the global estimation precision is higher than the local estimation precision. In the parameter limit condition, the precision of parameter estimation for the simultaneous estimation of each parameter is equal to the precision of the singleparameter estimation. In addition, we find a precision-enhancement scheme that depends on the dynamics SU(N). The smaller the N for the dynamics evolution, the higher the precision of the parameter estimation. Finally, we prove that the graph state is the optimal state of quantum metrology, a set of optimal measurement basic can be found, and the precision limit of multiparameter estimation can attain the quantum Cramér-Rao bound.

David C. Collins, Michael R. Frey

Akio Fujiwara

Pieter Kok, Samuel L. Braunstein, Jonathan P. Dowling

We explore the intimate relationship between quantum lithography, Heisenberg-limited parameter estimation and the rate of dynamical evolution of quantum states. We show how both the enhanced accuracy in measurements and the increased resolution in quantum lithography follow from the use of entanglement. Mathematically, the hyperresolution of quantum lithography appears naturally in the derivation of Heisenberg-limited parameter estimation. We also review recent experiments offering a proof of principle of quantum lithography, and we address the question of state preparation and the fabrication of suitable photoresists.

Jun O. S. Yin

Yu Yang, Haidong Yuan, Fuli Li

In quantum multiparameter estimation, multiple to-be-estimated parameters are encoded in a quantum dynamics system by a unitary evolution. As the parameters vary, the system may undergo a topological phase transition (TPT). In this paper, we investigate two SU(2) TPT models and propose the singular behavior of the quantum metric tensor around the TPT point as a tool for the simultaneous optimal estimation of multiple parameters. We find that the proposed TPT sensing protocol can achieve the same metrology performance as the quantum-control-enhanced one. Moreover, the probe state of the TPT sensing protocol is only the ground state of the Hamiltonian rather than the entangled state required in the control-enhanced one. In addition, an adaptive multiparameter estimation strategy is developed for updating the estimated values until the desired quantum Cram\'er-Rao bound is approached. Our work reinforces the connection between quantum multiparameter estimation and topology physics, with potential inspiration for quantum critical metrology.