Local discrimination of four or more maximally entangled states

In the 4 circle times 4 quantum system, four qubit lattice states are found to be either locally indistinguishable or distinguishable by using one-way classical communication only, presenting a curious and counterintuitive case in which two-way classical communication has no advantage. Based on these results, we explicitly construct sets of four, five, and even more maximally entangled states that can be locally distinguished only with the help of two-way classical communication, solving partially the open problem described by Nathanson [Phys. Rev. A 88, 062316 (2013)] and highlighting in more detail the difference between local operations with and without two-way classical communication in distinguishing more than three states.