Local indistinguishability of orthogonal pure states by using a bound on distillable entanglement
Sibasish Ghosh, Guruprasad Kar, Anirban Roy, Debasis Sarkar, Aditi Sen, Ujjwal Sen · Physical Review A · 2002
We show that the four states $a|00〉+b|11〉, \overline{b}|00〉\ensuremath{-}\ifmmode \bar{a}\else \={a}\fi{}|11〉, c|01〉+d|10〉,$ and $\overline{d}|01〉\ensuremath{-}\overline{c}|10〉$ 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.