Are there separable states $\rho$ that cannot be decomposed with less than $\operatorname{rank}(\rho)^2$ pure product states?

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edited May 16 at 10:29

Are there separable states $\rho$ that cannot be decomposed with separable pure decompositions requiring exactlyless than $\operatorname{rank}(\rho)^2$ componentspure product states?

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edited May 16 at 9:32

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edited Jan 30, 2023 at 10:18

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edited Apr 5, 2022 at 13:12

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asked Apr 5, 2022 at 12:42

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