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arXiv:2405.20296 · Scientific Reports

Critical metrology of minimally accessible anisotropic spin chains

Marco Adani, Simone Cavazzoni, Berihu Teklu, Paolo Bordone, Matteo G. A. Paris

Published Aug 27, 2024• 24 citations
arXivHTMLPDF

Abstract

We address quantum metrology in critical spin chains with anisotropy and Dzyaloshinskii-Moriya (DM) interaction, and show how local and quasi-local measurements may be exploited to characterize global properties of the systems. In particular, we evaluate the classical (magnetization) and quantum Fisher information of the relevant parameters for the density matrix of a single spin and that of a pair of spins ranging from nearest to sixth-nearest neighbors, to the limiting case of very distant spins. Our results allow us to elucidate the role of the different parameters and to individuate the optimal working regimes for the precise characterization of the system, also clarifying the effects of correlations on the estimation precision.

DOI
10.1038/s41598-024-70307-8

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We address quantum metrology in critical spin chains with anisotropy and Dzyaloshinskii-Moriya (DM) interaction, and show how local and quasi-local measurements may be exploited to characterize global properties of the systems. In particular, we evaluate the classical (magnetization) and quantum Fisher information of the relevant parameters for the density matrix of a single spin and that of a pair of spins ranging from nearest to sixth-nearest neighbors, to the limiting case of very distant spins. Our results allow us to elucidate the role of the different parameters and to individuate the optimal working regimes for the precise characterization of the system, also clarifying the effects of correlations on the estimation precision.
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We theoretically investigate quantum parameter estimation in a two-qubit anisotropic Heisenberg spin system with Dzyaloshinskii-Moriya (DM) interaction in the presence of intrinsic decoherence described by the Milburn model. Using the Quantum Fisher Information (QFI), we study the estimation of both the uniform magnetic field and the DM interaction strength. Analytical expressions for the time-evolved density matrix are obtained and used to explore the effects of exchange anisotropy, intrinsic decoherence, and probe-state preparation on the achievable estimation precision. Our results show that suitable tuning of the anisotropic exchange coupling and the initial entangled state can considerably enhance the estimation performance, with different optimal parameter regimes emerging for magnetic-field and DM-interaction sensing. To better understand the role of quantum resources in metrology, we also examine the behaviour of concurrence, quantum coherence, and von Neumann entropy. Overall, our findings demonstrate that anisotropic Heisenberg spin systems with DM interaction provide a promising and flexible platform for high-precision quantum metrology even in the presence of intrinsic decoherence.
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We study the relationship between the quantum Fisher information (QFI) of spin pairs and the topological quantum phase transitions (TQPTs) of the extended XY model driven by the anisotropies of the nearest-neighbor and the next-nearest-neighbor spins, the transverse magnetic field, and the three-spin interaction. We find that the first derivative of QFI can correctly characterize the TQPTs at absolute zero temperature. Meanwhile, the impacts of the thermal fluctuations and the site distance of spin pairs on the critical behaviors of the QFI are studied. It is found that the first derivative of QFI for the nearest neighbor or the long-distance spin pairs can only correctly characterize the critical points of the TQPTs at sufficiently low temperature. Remarkably, when the anisotropy of the nearest-neighbor and the next-nearest-neighbor spins are the driven parameters and the site distance R=5R=5R=5, the QFI itself can characterize the TQPTs at absolute zero temperature.
We study the effect of Dzyaloshinskii-Moriya (DM) interaction on pairwise quantum discord, entanglement, and classical correlation in the anisotropic XY\mathrm{XY}XY spin-half chain. Analytical expressions for both quantum and classical correlations are obtained from the spin-spin correlation functions. These pairwise quantities exhibit interesting behaviors in relation to the relative strengths of the physical parameters. For the infinite chain, we show that the quantum discord can be useful to highlight the quantum phase transition, especially for the long-distance spins, where entanglement decays rapidly. We observe nonanalyticities of the derivatives of both quantum and classical correlations with respect to the magnetic intensity at the critical point; interestingly, the DM interaction weakens the critical behavior in the derivatives of these correlations. While the DM interaction suppresses the standard behaviors of the XY\mathrm{XY}XY model, it enhances surprisingly the pairwise entanglement for the third nearest neighbor spins.