Measures from conical 2-designs depend only on two constants

Abstract Quantum measurements are important tools in quantum information, represented by positive, operator-valued measures. A wide class of symmetric measurements is given via generalized equiangular measurements that form conical 2-designs. We show that only two positive constants are needed to fully characterize a variety of important quantum measures constructed from such operators. Examples are given for entropic uncertainty relations, the Brukner-Zeilinger invariants, quantum coherence, quantum concurrence, and the Schmidt-number criterion for entanglement detection. Our results indicate that similar relations may also hold for conical 2-designs from beyond the class of generalized equiangular measurements.