One-way LOCC indistinguishability of maximally entangled states

In this letter, we mainly study the local indistinguishability of mutually orthogonal maximally entangled states, which are in canonical form. Firstly, we present a feasible sufficient and necessary condition for distinguishing such states by one-way local operations and classical communication (LOCC). Secondly, for the application of this condition, we exhibit one class of maximally entangled states that can be locally distinguished with certainty. Furthermore, sets of d - 1 indistinguishable maximally entangled states by one-way LOCC are demonstrated in d circle times d (for d = 7, 8, 9, 10). Interestingly, we discover there exist sets of d - 2 such states in d circle times d (for d = 8, 9, 10), which are not perfectly distinguishable by one-way LOCC. Finally, we conjecture that there exist d - 1 or fewer indistinguishable maximally entangled states in d circle times d (d >= 5) by one-way LOCC.