  We show that the four states a|00>+b|11>, b^*|00>-a^*|11>, c|01>+d|10> and
d^*|01>-c^*|10> cannot be discriminated with certainty if only local operations
and classical communication (LOCC) are allowed and if only a single copy is
provided, except in the case when they are simply |00>, |11>, |01> and |10> (in
which case they are trivially distinguishable with LOCC). We go on to show that
there exists a continuous range of values of a, b, c and d such that even three
states among the above four are not locally distinguishable, if only a single
copy is provided. The proof follows from the fact that logarithmic negativity
is an upper bound of distillable entanglement.
