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

TL;DR

This paper introduces a broad class of indecomposable exposed positive maps for 3x3 matrices and constructs specific separable states, revealing that mixing can reduce their length.

Contribution

It provides new examples of indecomposable exposed positive maps and separable states, demonstrating the effect of mixing on the length of separable states.

Findings

Constructed two qutrit separable states with length ten.

Showed that mixing can strictly decrease the length of a separable state.

Presented a large class of indecomposable exposed positive maps.

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.