• 실적년도 : 2014
• 논문구분 : 국외
• 총저자 : Zenon Jablonski, Il Bong Jung, Jan Stochel
• 학술지명 : Integral Equations and Operator Theor
• 권(Vol.) : 79
• 호(No.) : 2014
• 게재년월 : 2014년 5월
• IF : 0.583(jcr2013)
• SCI 등재 : SCI
• 국제공동연구 논문여부 : O
• 기여도 : 40%
• Abstract : We search for faces of the convex set consisting of all separable states,
  which are affinely isomorphic to simplices, to get separable states with unique decompositions.
  In the two-qutrit case, we found that six product vectors spanning a five
  dimensional space give rise to a face isomorphic to the 5-dimensional simplex with six
  vertices, under suitable linear independence assumption. If the partial conjugates of
  six product vectors also span a 5-dimensional space, then this face is inscribed in the
  face for PPT states whose boundary shares the fifteen 3-simplices on the boundary of
  the 5-simplex. The remaining boundary points consist of PPT entangled edge states
  of rank four. We also show that every edge state of rank four arises in this way. If the
  partial conjugates of the above six product vectors span a 6-dimensional space then
  we have a face isomorphic to 5-simplex, whose interior consists of separable states
  with unique decompositions, but with non-symmetric ranks. We also construct a face
  isomorphic to the 9-simplex. As applications, we give answers to questions in the
  literature [8, 9], and construct 3 ⊗ 3 PPT states of type (9,5). For the qubit-qudit
  cases with d ≥ 3, we also show that (d + 1)-dimensional subspaces give rise to faces
  isomorphic to the d-simplices, in most cases.

Separable states with unique decompositions.pdf