Quantum phase estimations with spin coherent states superposition

The quantum metrological performance of spin coherent states superposition is considered, and conditions for measurements with the Heisenberg-limit (HL) precision are identified. It demonstrated that choice parameter-generating operator can lead to physically different estimation outcomes. In particular, closed-form analytical descriptions cat derived. These findings show routes careful control parameters necessary achieving HL provide insightful information on geometry specific state its relevance parameter estimations.