IFIC Seminar: Optimal control for Hamiltonian metrology in dynamical and steady states

por Paolo Abiuso (IQOQI - Vienna)

martes 28 oct. 2025 12:00 → 13:00 Europe/Madrid

Primera-1-1-1 - Paterna. Seminario (IFIC)

The standard goal of metrology is that of estimating a parameter θ encoded in the (generally quantum) physical state of a system. It is known that the optimal precision achievable can be quantified by a geometric notion of information, namely the quantum Fisher information (QFI in short), which depends on how the state of the system depends on θ.
In this talk, we study the problem of optimal metrology when given partial Hamiltonian control on a quantum system. We do this by maximising the QFI for relevant classes of states:  that is, we take a generic Hamiltonian H(θ)=HP(θ)+HC  which is divided into a fixed parameter-encoding term HP(θ) and an externally controllable HC. In different scenarios, we maximise the QFI with respect to HC . Specifically, we consider:
1) Dynamical states, i.e. those evolving according to the unitary evolution generated by the global H(θ) [1]
2) Steady states, in particular dephased states and thermal states according to H(θ) [1,2]
3) Intermediate noisy regimes [1]
We provide simple analytical expressions for the QFI of these classes of states, the analytical solutions to the QFI maximisation and the opimal HC that are needed to saturate it. In all cases, we assume reasonable initial resources (such as initially separable states and/or and HC based on two-body interactions only), highlighting the power of realistic Hamiltonian control in quantum metrology. We study the scaling of the QFI in the number of particles N and find that Heisenberg-like N2 scaling are recovered also when using initially separable states in [3], and also with semi-classically dephased states and thermal state that do not feature entanglement [2]. We highlight the properties and spectra of the optimally-controlled Hamiltonians. Finally, we also consider the closely-related case of temperature estimation in thermal states, which has been solved some years ago [3]: we show how similar scaling properties and optimality hold for thermometry under the assumption of two-body interactions [4].

References
[1] Puig R, Sekatski P, Erdman PA, Abiuso P, Calsamiglia J, Perarnau-Llobet M. From dynamical to steady-state many-body metrology: Precision limits and their attainability with two-body interactions. PRX Quantum, 2025; 6 (3), 030309
[2] Abiuso P, Sekatski P, Calsamiglia J, Perarnau-Llobet M. Fundamental limits of metrology at thermal equilibrium. Physical Review Letters. 2025;134(1):010801.
[3] Correa LA, M Mehboudi M, Adesso G, Sanpera A, Individual quantum probes for optimal thermometry. Physical review letters 2015, 114(22), p.220405.
[4] Abiuso P, Erdman PA, Ronen M, Noé F, Haack G, Perarnau-Llobet M. Optimal thermometers with spin networks. Quantum Science and Technology 2024. 9 (3), 035008