For any bipartite quantum system the Schmidt decomposition allows us to exp
ress a pure state vector in terms of a single sum instead of double sums. I
t is shown that if the partial inner product of a basis (belonging to a Hil
bert space of smallest dimension) with the state of the composite system gi
ves a disentangled basis then the Schmidt decomposition exists for triparti
te system. In this case the reduced density matrix of each of the subsystem
has equal spectrum in the Schmidt basis. (C) 2000 Elsevier Science B.V. Al
l rights reserved.