The Brukner-Zeilinger invariants in terms of (N, M) − POVMs

Abstract Brukner–Zeilinger invariants, including invariant information and invariant uncertainty, play a remarkable role in quantum information theory. Recently, a broad class of symmetric informationally complete measurements is presented, which contains a general symmetrical information complete POVMs and mutually unbiased measurements (2022, Phys. Rev. A 105 , 042 209). Based on this important measurement and variance, we further analyze the internal relationship between Brukner–Zeilinger invariants in detail. The results maybe provide a method to explain the importance of Brukner–Zeilinger invariants.