Separable positive operator (${\eta }_{AB}$)

A separable positive operator is a finite sum ${\eta }_{AB}={\sum }_y{\alpha }_y\otimes {\beta }_y$ with both factors positive operators. If its trace is one, normalizing the nonzero factors gives a separable quantum state. Conversely, a nonnegative scalar multiple of a separable quantum state is a separable positive operator.