  It is shown that the order property of pure bipartite states under SLOCC
(stochastic local operations and classical communications) changes radically
when dimensionality shifts from finite to infinite. In contrast to finite
dimensional systems where there is no pure incomparable state, the existence of
infinitely many mutually SLOCC incomparable states is shown for infinite
dimensional systems even under the bounded energy and finite information
exchange condition. These results show that the effect of the infinite
dimensionality of Hilbert space, the ``infinite workspace'' property, remains
even in physically relevant infinite dimensional systems.
