Positive-partial-transpose distinguishability for lattice-type maximally entangled states

Abstract

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.

It's rewritten. We deleted the original section II about PPT-distinguishability of three ququad-ququad MESs. Moreover, we have joined new section V which discuss PPT-distinguishability of lattice MESs for cases $t=3$ and $t=4$ . As a result, the sequence of the theorems in our article has been changed. And we revised the title of our article

References in corpus (1)

• $d$ locally indistinguishable maximally entangled states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$

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• Strong quantum nonlocality and unextendibility without entanglement in $N$-partite systems with odd $N$
• Graph connectivity based strong quantum nonlocality with genuine entanglement