Universal Markov Kernels for quantum observables

Abstract

We prove the existence of a universal Markov kernel, i.e., a Markov kernel µ such that every commutative POVM F is the smearing of a selfadjoint operator A F with the smearing realized through µ. The relevance of the smearing is illustrated in connection with the problem of the joint measurability of two quantum observables. Also the connections with phase space quantum mechanics is outlined.