  We investigate the problem of the existence of a density matrix rho on the
product of three Hilbert spaces with given marginals on the pair (1,2) and the
pair (2,3). While we do not solve this problem completely we offer partial
results in the form of some necessary and some sufficient conditions on the two
marginals. The quantum case differs markedly from the classical (commutative)
case, where the obvious necessary compatibility condition suffices, namely,
trace_1 (rho_{12}) = \trace_3 (rho_{23}).
