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

TL;DR

This paper investigates the local distinguishability of lattice-type maximally entangled states using semidefinite programming, identifying sets of states that are either distinguishable or indistinguishable under local operations.

Contribution

It introduces a new semidefinite programming approach to analyze PPT-distinguishability of lattice maximally entangled states and constructs specific sets with known distinguishability properties.

Findings

Constructed all sets of four orthogonal lattice states that are locally indistinguishable.

Identified sets of six lattice states with interesting distinguishability properties.

Resolved some open problems regarding PPT-distinguishability of lattice 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.