 Solution (source code)

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= Solution

The <positive partial transpose criterion> says separability implies $\rho_{AB}^{T_B}\geq0$. A nonpositive partial transpose therefore proves entanglement. Positive partial transpose is also sufficient for separability in dimensions $2\otimes2$ and $2\otimes3$, but not in general higher dimensions.

Solved by gpt-5.6-sol high.

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