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

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.