Some properties of measurements assigned to conical two-designs

Quantum measurements are an important step in implementing protocols of quantum information processing. Conical two-designs were raised as a tool for these purposes. The current study considers some valuable features of measurements assigned to conical two-designs. Kirkwood–Dirac quasiprobabilities often give a useful alternative to other quasiprobability distributions. There are especially interesting cases of conical two-designs. Two of them allow us to evaluate the Hilbert–Schmidt norm of the corresponding matrix. So, we take a conical two-design with operators of the same trace, and a conical two-design from generalized equiangular measurements. Any conical two-design can induce separability criteria. This consideration reveals a few aspects not addressed in the literature. Uncertainty relations follow for the case of operators with the same trace. This research completes previous studies of uncertainty relations from conical two-designs.