Exposedness of Choi type entanglement witnesses and applications to lengths of separable states

Abstract

We present a large class of indecomposable exposed positive linear maps between three dimensional matrix algebras. We also construct two qutrit separable states with lengths ten in the interior of their dual faces. With these examples, we show that the length of a separable state may decrease strictly when we mix it with another separable state.

15 pages, minor revision

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Cited by in corpus (9)

• Entanglement witnesses: construction, analysis and classification
• Entanglement witnesses from mutually unbiased bases
• Dimensions, lengths and separability in finite-dimensional quantum systems
• Three-qubit entanglement witnesses with the full spanning properties
• Boundary of the set of separable states
• Faces for two qubit separable states and the convex hulls of trigonometric moment curves
• Merging of positive maps: a construction of various classes of positive maps on matrix algebras
• Global geometric difference between separable and Positive partial transpose states
• Notes on extremality of the Choi map