We study the distinguishability of a particular type of maximally entangled states -- the lattice states using a new approach of semidefinite program. With this, we successfully construct all sets of four ququad-ququad orthogonal maximally entangled states that are locally indistinguishable and find some curious sets of six states having interesting property of distinguishability. Also, some of the problems arose from cite{CosentinoR14} about the PPT-distinguishability of lattice maximally entangled states can be answered.
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