Three-qubit separable states of length ten with unique decompositions
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We construct one-parameter families of three-qubit separable states with length ten, which is strictly greater than the whole dimension eight. These states are located on the boundary of the convex set of all separable states, but they are in the interior of the convex set of all states with positive partial transposes. They are also decomposed into the convex sum of ten pure product states in a unique way.
KeywordsLengths of separable states Three-qubit states Unique decomposition Positive multi-linear maps Dual faces
Mathematics Subject Classification81P15 15A30 46L07
The author is grateful to Kyung Hoon Han for valuable comments and discussion.
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