Metrological usefulness of entanglement and nonlinear Hamiltonians

Year: 2025

Authors: Imai S., Smerzi A., Pezzè L.

Autors Affiliation: QSTAR, INO CNR, Largo Enr Fermi 2, I-50125 Florence, Italy; LENS, Largo Enr Fermi 2, I-50125 Florence, Italy.

Abstract: A central task in quantum metrology is to exploit quantum correlations to outperform classical sensitivity limits. Metrologically useful entanglement is identified when the quantum Fisher information (QFI) exceeds a separability bound for a given parameter-encoding Hamiltonian. However, so far, only results for linear Hamiltonians are well established. Here, we characterize metrologically useful entanglement for nonlinear Hamiltonians, presenting separability bounds for collective angular momenta. Also, we provide a general expression for entangled states maximizing the QFI, which can be written as the superposition between the Greenberger-Horne-Zeilinger-like and singlet states. Finally, we compare the metrological usefulness of linear and nonlinear cases, in terms of entanglement detection and random symmetric states.

Journal/Review: PHYSICAL REVIEW A

Volume: 111 (2)      Pages from: L020402-1  to: L020402-7

More Information: We would like to thank Francesco Albarelli, Stefano Gherardini, Vittorio Giovannetti, Otfried Guhne, Ties Ohst, Hai-Long Shi, Geza Toth, and Benjamin Yadin for discussions. This work has received funding under Horizon Europe programme HORIZON-CL4-2022-QUANTUM-02-SGA via Project No. 101113690 (PASQuanS2.1) and by the European Commission through the H2020 QuantERA ERA-NET Cofund in Quantum Technologies projects SQUEIS.
KeyWords: Ground-state; Quantum; Decoherence; Information; Matter; Error
DOI: 10.1103/PhysRevA.111.L020402