Facial structures of separable and PPT states

• Autorzy: Seung-Hyeok Kye
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46L05: General theory of C * -algebras
• 81P15: Quantum measurement theory
• 15A30: Algebraic systems of matrices

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 96
• Numer: 1
• Strony: 257-269

Daty

wydano

2011

Twórcy

autor

Seung-Hyeok Kye

• Department of Mathematics, Seoul National University, Seoul 151-742, Korea

Identyfikatory

DOI

10.4064/bc96-0-17