Solution (source code)

= Solution

The <positive partial transpose criterion> states that every <separable quantum state> satisfies
$$
\rho_{AB}^{T_B}\geq0.
$$
Consequently, a negative <eigenvalue> of the <partial transpose> proves entanglement. Positivity of the partial transpose is also sufficient for separability in dimensions $2\otimes2$ and $2\otimes3$, equivalently $3\otimes2$, but it is not sufficient in general higher dimensions.