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arXiv · 2402.07089

Quantum multiparameter estimation enhanced by a topological phase transition

Yu Yang·Haidong Yuan·Fuli Li
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Abstract

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.

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Yu Yang, Haidong Yuan, Fuli Li. 2024-02-11. Quantum multiparameter estimation enhanced by a topological phase transition. https://doi.org/10.1103/physreva.109.022604

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