Rina Miyajima

Phase estimation serves as a unifying framework for precision measurements in physics. While protocols using Greenberger-Horne-Zeilinger (GHZ) states can achieve the Heisenberg limit, they require prior knowledge of the Hamiltonian to align the probe's sensitivity axis. This necessity for precise alignment imposes a burden on the state preparation stage, limiting practical applications where the field direction is unknown or fluctuating. In this work, we address this limitation by identifying the symmetric subspace as a source of universal metrological resources. We introduce the concept of universal resource states (URS), a class of probe states capable of achieving Heisenberg-limited precision for any linear collective Hamiltonian, independent of its orientation. Our contribution is the explicit analytical derivation of these states and proving that almost all symmetric states serve as URSs for all linear collective Hamiltonians simultaneously. This reveals the symmetric subspace as an inherent reservoir of universal metrological resources: a single, generic symmetric state suffices for high-precision metrology, enabling state preparation completely decoupled from the Hamiltonian's orientation.