  In this letter we have established the physical character of pure bipartite
states with the same amount of entanglement in the same Schmidt rank that
either they are local unitarily connected or they are incomparable. There exist
infinite number of deterministically locally inequivalent classes of pure
bipartite states in the same Schmidt rank (starting from three) having same
amount of entanglement. Further, if there exists incomparable states with same
entanglement in higher Schmidt ranks (greater than three), then they should
differ in at least three Schmidt coefficients.
