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arXiv:2405.15703 · Physical Review A

Metrological usefulness of entanglement and nonlinear Hamiltonians

Satoya Imai, Augusto Smerzi, Luca Pezzè

Published Feb 10, 2025• 9 citations
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Abstract

The authors establish metrological criteria for entanglement in quantum systems with nonlinear Hamiltonians, deriving separability bounds for quantum Fisher information. Their findings reveal classes of entangled states beyond GHZ-like structures, offering insights into the metrological advantages of nonlinear dynamics.
DOI
10.1103/physreva.111.l020402

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Quantum metrology faces major challenges in noisy environments, where decoherence rapidly degrades useful quantum resources. We investigate the dynamics of the precision limits given by the quantum Fisher information (QFI) for phase estimation under spatially correlated dephasing. We characterize the dynamics of the QFI by the sensitivity and degradation indicators that can be obtained as analytical expressions derived using perturbative theory treatment. These short-time and weak-noise formulas yield analytic insight into how collective-spin moments govern both (i) the noiseless sensitivity and (ii) the leading noise-induced degradation of metrological usefulness. We identify a trade-off that is intrinsic to our commuting encoding-noise structure. We analyze the QFI dynamics for the Gaussian spin state (GSS) superpositions, encompassing spin coherent state (SCS), Dicke state superpositions, spin-squeezed states, and GHZ-like states. Predictions from indicators of the QFI dynamics are compared to both the quantum Cramér--Rao bound and the measurement-specific sensitivity bounds for an optimal parameter and interrogation time under a finite total time resource. When possible, we analytically derive the measurement-specific sensitivity bounds for spin-projection and parity-based measurements.