Quartic Certificates for Pure-State Tomography with Pauli Measurements
The paper investigates how to determine if every quantum state is uniquely identifiable using only a subset of Pauli measurements. It introduces a 'quartic certificate' based on the fourth elementary symmetric polynomial of omitted observables. This certificate provides structural criteria to guarantee universal uniqueness (UDA) or uniqueness among pure states (UDP), offering checkable rules for certifying pure-state tomography from restricted measurements.