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J. Korean Math. Soc. 2012; 49(3): 623-639

Printed May 1, 2012

https://doi.org/10.4134/JKMS.2012.49.3.623

Copyright © The Korean Mathematical Society.

Facial structures for separable states

Hyun-Suk Choi and Seung-Hyeok Kye

Seoul National University, Seoul National University

Abstract

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The convex cone $\mathbb V_1$ generated by separable states is contained in the cone $\mathbb T$ of all positive semi-definite block matrices whose block transposes are also positive semi-definite. We characterize faces of the cone $\mathbb V_1$ induced by faces of the cone $\mathbb T$ which are determined by pairs of subspaces of matrices.

Keywords: separable states, faces, entanglement

MSC numbers: 81P15, 46L05, 15A30

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