Description of rank four PPT entangled states of two qutrits
Lin Chen, Dragomir Z. Djokovic
TL;DR
This paper proves that all rank four PPT entangled states of two qutrits can be constructed from unextendible product bases and classifies certain subspaces with finitely many product states.
Contribution
It establishes the universality of UPB-based construction for rank four PPT entangled states and classifies relevant subspaces.
Findings
All rank four PPT entangled states of two qutrits can be constructed from UPB.
Classified 5-dimensional subspaces with finitely many product states.
Identified subspaces spanned by UPB.
Abstract
It is known that some two qutrit entangled states of rank 4 with positive partial transpose [PPT] can be built from the unextendible product bases [UPB]. We show that this fact is indeed universal, namely all such states can be constructed from UPB. We also classify the 5-dimensional subspaces of two qutrits which contain only finitely many product states (up to scalar multiple), and in particular those spanned by a UPB.
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