Quantum enhancement in magnetic field precision in partially accessible quantum many-body systems by a periodic driving

The criticality of the ground state of many-body systems is a potential resource for quantum-enhanced sensing, namely the Heisenberg precision limit. This enhancement depends on the accessibility of the whole system. We demonstrate that for partial accessibility, the data gathered by measuring a block of spins in the ground state reduces the sensing capability to the sub-Heisenberg limit. To compensate for this, we propose a driving protocol consisting of measurement on local steady-state for quantum sensing. Remarkably, the steady-state sensing shows a significant enhancement in precision compared to the ground state and even achieves super-Heisenberg scaling for low frequencies. We use this method and infer the magnetic field with the Heisenberg scaling. The origin of this precision enhancement is related to the closing of the Floquet quasienergy gap. It is in close correspondence with the vanishing of the energy gap at criticality for ground state sensing with global accessibility. The proposal is general to all the integrable models and can be implemented on existing quantum devices.