Local indistinguishability of orthogonal pure states by using a bound on distillable entanglement

We show that the four states a\00>+b\11>, (b) over bar \00>-(a) over bar \11>, c\01>+d\10>, and (d) over bar \01>-(c) over bar \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.