Entanglement witnesses arising from Choi type positive linear maps

Abstract

We construct optimal PPTES witnesses to detect $3\otimes 3$ PPT entangled edge states of type $(6,8)$ constructed recently \cite{kye_osaka}. To do this, we consider positive linear maps which are variants of the Choi type map involving complex numbers, and examine several notions related to optimality for those entanglement witnesses. Through the discussion, we suggest a method to check the optimality of entanglement witnesses without the spanning property.

18 pages, 4 figures, 1 table

References in corpus (5)

• Structural approximations to positive maps and entanglement breaking channels
• Optimality for indecomposable entanglement witnesses
• A characterization of optimal entanglement witnesses
• Classification of bi-qutrit positive partial transpose entangled edge states by their ranks
• The structural physical approximations and optimal entanglement witnesses

Cited by in corpus (8)

• Facial structures for various notions of positivity and applications to the theory of entanglement
• Entanglement witnesses from mutually unbiased bases
• The structural physical approximations and optimal entanglement witnesses
• Exposedness of Choi type entanglement witnesses and applications to lengths of separable states
• Extremal extensions of entanglement witnesses and their connection with UPB
• Extremal entanglement witnesses
• Constructing positive maps from block matrices
• Global geometric difference between separable and Positive partial transpose states