Brukner–Zeilinger invariant information

We present an alternative interpretation of the notion of invariant information by establishing that it is directly related to the total ordinary variance of a quantum state. Here, "total" means summing the variance over any complete orthogonal set of observables or, equivalently, averaging over a certain sufficiently general ensemble of the observables. This simple, intuitive substratum of the Brukner–Zeilinger invariant information sheds further light on the informational and statistical nature of quantum measurements.