  We prove that the standard quantum mechanical description of a quantum state
change due to measurement, given by Lueders' rules, is a special case of the
constrained maximisation of a quantum relative entropy functional. This result
is a quantum analogue of the derivation of the Bayes--Laplace rule as a special
case of the constrained maximisation of relative entropy. The proof is provided
for the Umegaki relative entropy of density operators over a Hilbert space as
well as for the Araki relative entropy of normal states over a W*-algebra. We
also introduce a quantum analogue of Jeffrey's rule, derive it in the same way
as above, and discuss the meaning of these results for quantum bayesianism.
