  In the topic of perfect local distinguishability of orthogonal multipartite
quantum states, most results obtained so far pertain to bipartite systems whose
subsystems are of specific dimensions. In contrast very few results for
bipartite systems whose subsystems are of arbitrary dimensions, are known. This
is because a rich variety of (algebraic or geometric) structure is exhibited by
different sets of orthogonal states owing to which it is difficult to associate
some common property underlying them all, i.e., a common property that would
play a crucial role in the local distinguishability of these states. In this
paper, I propose a framework for the distinguishability by one-way LOCC
($1$-LOCC) of sets of orthogonal bipartite states in a $d_A \otimes d_B$
bipartite system, where $d_A, d_B$ are the dimensions of both subsytems,
labelled as $A$ and $B$. I show that if the $i$-th party (where $i=A,B$) can
initiate a $1$-LOCC protocol to perfectly distinguish among a set of orthogonal
bipartite states, then the information of the existence of such a $1$-LOCC
protocol lies in a subspace of $d_i \times d_i$ hermitian matrices, denoted by
$\Tb^{(i)}$, and that the method to extract this information (of the existence
of this $1$-LOCC protocol) from $\Tb^{(i)}$ depends on the value of $dim
\Tb^{(i)}$. In this way one can give sweeping results for the $1$-LOCC
(in)distinguishability of all sets of orthogonal bipartite states corresponding
to certain values of $dim \Tb^{(i)}$. Thus I propose that the value of $dim
\Tb^{(i)}$ gives the common underlying property based on which sweeping results
for the $1$-LOCC (in)distinguishability of orthogonal bipartite quantum states
can be made.
