Facial structures of separable and PPT states

Seung-Hyeok Kye

Banach Center Publications (2011)

  • Volume: 96, Issue: 1, page 257-269
  • ISSN: 0137-6934

Abstract

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A positive semi-definite block matrix (a state if it is normalized) is said to be separable if it is the sum of simple tensors of positive semi-definite matrices. A state is said to be entangled if it is not separable. It is very difficult to detect the border between separable and entangled states. The PPT (positive partial transpose) criterion tells us that the partial transpose of a separable state is again positive semi-definite, as was observed by M. D. Choi in 1982 from the mathematics side. In this expository note, we explain the facial structures of the cone of all PPT block matrices, which are naturally characterized by pairs of subspaces of (small) matrices. We also discuss which faces of PPT's induce faces of separables, and which faces of separables are induced by PPT's.

How to cite

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Seung-Hyeok Kye. "Facial structures of separable and PPT states." Banach Center Publications 96.1 (2011): 257-269. <http://eudml.org/doc/282274>.

@article{Seung2011,
abstract = { A positive semi-definite block matrix (a state if it is normalized) is said to be separable if it is the sum of simple tensors of positive semi-definite matrices. A state is said to be entangled if it is not separable. It is very difficult to detect the border between separable and entangled states. The PPT (positive partial transpose) criterion tells us that the partial transpose of a separable state is again positive semi-definite, as was observed by M. D. Choi in 1982 from the mathematics side. In this expository note, we explain the facial structures of the cone of all PPT block matrices, which are naturally characterized by pairs of subspaces of (small) matrices. We also discuss which faces of PPT's induce faces of separables, and which faces of separables are induced by PPT's. },
author = {Seung-Hyeok Kye},
journal = {Banach Center Publications},
keywords = {entanglement; positive partial transpose; positive linear maps; decomposable maps; faces},
language = {eng},
number = {1},
pages = {257-269},
title = {Facial structures of separable and PPT states},
url = {http://eudml.org/doc/282274},
volume = {96},
year = {2011},
}

TY - JOUR
AU - Seung-Hyeok Kye
TI - Facial structures of separable and PPT states
JO - Banach Center Publications
PY - 2011
VL - 96
IS - 1
SP - 257
EP - 269
AB - A positive semi-definite block matrix (a state if it is normalized) is said to be separable if it is the sum of simple tensors of positive semi-definite matrices. A state is said to be entangled if it is not separable. It is very difficult to detect the border between separable and entangled states. The PPT (positive partial transpose) criterion tells us that the partial transpose of a separable state is again positive semi-definite, as was observed by M. D. Choi in 1982 from the mathematics side. In this expository note, we explain the facial structures of the cone of all PPT block matrices, which are naturally characterized by pairs of subspaces of (small) matrices. We also discuss which faces of PPT's induce faces of separables, and which faces of separables are induced by PPT's.
LA - eng
KW - entanglement; positive partial transpose; positive linear maps; decomposable maps; faces
UR - http://eudml.org/doc/282274
ER -

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