If a POVM consists of at least d 2 operators which span the space of self-adjoint operators L ( H ) , it is said to be an informationally complete POVM (IC-POVM). IC-POVMs consisting of exactly d 2 elements are called minimal. A set of d 2 rank -1 projectors { Π Π i } i = 1 d 2 which have equal pairwise Hilbert–Schmidt inner products, T r ( Π Π i Π Π j ) = d δ δ i j + 1 d + 1 , defines a minimal IC-POVM with elements F i = 1 d Π Π i called a SIC-POVM.