Relating measurement disturbance, information, and orthogonality

In the general theory of quantum measurement, one associates a positive-semidefinite operator on $d$-dimensional Hilbert space to each $n$ possible outcomes an arbitrary measurement. special case projective these operators are pairwise Hilbert-Schmidt orthogonal, but when $n>d$, orthogonality is restricted by positivity. This restriction allows us more precisely state adage: information gain system always accompanied unavoidable disturbance. Specifically, we investigate three properties measurement with L\"uders rule updating: its disturbance, measure how expected postmeasurement deviates from input; strength, intrinsic producing capacity measurement; and orthogonality, degree which differ orthonormal set. These quantities satisfy information-disturbance tradeoff relation that highlights additional role played orthogonality. Finally, assess several classes measurements grounds identify symmetric informationally complete as unique analogs perfectly informative nondisturbing classical ideal