Entanglement swapping between multi-qudit systems

We generalize the entanglement swapping scheme originally proposed for two pairs of qubits to an arbitrary number q of systems composed from an arbitrary number m(j) of qudits. Each of the systems is supposed to be prepared in a maximally entangled state of mi qudits, while different systems are not correlated at all. We show that when a set of Sigma (q)(j=1)a(j) particles (from each of the q systems a(j) particles are measured) is subjected to a generalized Bell-type measurement, the resulting set of Sigma (q)(j=1)(m(j)-a(j)) particles will collapse into a maximally entangled state.