  The (im)possibility of local distinguishability of orthogonal multipartite
quantum states still remains an intriguing question. Beyond
$\mathbb{C}^{3}\otimes\mathbb{C}^{3}$, the problem remains unsolved even for
maximally entangled states (MES). So far, the only known condition for the
local distinguishability of states is the well-known orthogonality preservation
(OP). Using an upper bound on the locally accessible information for bipartite
states, we derive a very simple necessary condition for any set of pairwise
orthogonal MES in $\mathbb{C}^{d}\otimes \mathbb{C}^{d}$ to be perfectly
locally distinguishable. This condition is seen to be stronger than the OP
condition. This is particularly so for any set of $d$ number of pairwise
orthogonal MES in $\mathbb{C}^{d}\otimes \mathbb{C}^{d}$. When testing this
condition for the local distinguishability of all sets of four generalized Bell
states in $\mathbb{C}^{4}\otimes \mathbb{C}^{4}$, we find that it is not only
necessary but also sufficient to determine their local distinguishability. This
demonstrates that the aforementioned upper-bound may play a significant role in
the general scenario of local distinguishability of bipartite states.
