Metrological usefulness of entanglement and nonlinear Hamiltonians

TL;DR

This paper extends the understanding of quantum entanglement's role in metrology by analyzing nonlinear Hamiltonians, establishing bounds, and identifying states that optimize quantum Fisher information.

Contribution

It introduces separability bounds for nonlinear Hamiltonians and characterizes states that maximize quantum Fisher information, advancing quantum metrology theory.

Findings

Derived separability bounds for nonlinear Hamiltonians.

Identified superpositions of GHZ-like and singlet states as optimal.

Compared linear and nonlinear Hamiltonian cases in entanglement usefulness.

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 GHZ-like and singlet states. Finally, we compare the metrological usefulness of linear and nonlinear cases, in terms of entanglement detection and random symmetric states.