From dynamical to steady-state many-body metrology: Precision limits and their attainability with two-body interactions

Understand

We consider the estimation of an unknown parameter $\theta$ via a many-body probe.

• The probe is initially prepared in a product state and many-body time-independent interactions enhance its $\theta$-sensitivity during the dynamics and/or in the steady state.
• We present bounds on the Quantum Fisher Information, and corresponding optimal interacting Hamiltonians, for two paradigmatic scenarios for encoding~$\theta$: (i)~via unitary Hamiltonian dynamics (dynamical metrology), and (ii)~in the Gibbs and diagonal ensembles (time-averaged dephased state), two ubiquitous steady states of many-body open dynamics.
• We then move to the specific problem of estimating the strength of a magnetic field via interacting spins and derive two-body interacting Hamiltonians that can approach the fundamental precision bounds.