Quantal Euclidean mappings

Given a set of non-commuting operators Ô1,…,ÔN, and the assumed knowledge of the expectation values of a subset containing just M of them, we discuss, in quite general terms, what can be predicted about the behaviour of the expectation values of the remaining operators when the concomitant wave functions are not available (not even in principle) because the pertinent hamiltonian is unknown. An RM→RN−M mapping ensues. Information theoretical tools are employed and some simple examples examined.