Mixture of entangled state can be separable state.

Theoretically we only directly have that mixture of separable state is separable state, and can say nothing about mixture of entangled state. The state set can be visualized as follows:

So we can see that we might have mixture of entangled state to be separable.

We can have an example that mixture of entangled state to be separable state: mixture of \(\rho _1\equiv p|{\psi _1}^-\rangle \langle {\psi _1}^-|+\frac{1-p}{4}I\) and \(\rho _2\equiv p|{\psi _2}^-\rangle \langle {\psi _2}^-|+\frac{1-p}{4}I\) to get \(\rho _3\equiv \frac{\rho _1}{2}+\frac{\rho _2}{2}\), where $|{\psi _1}^-\rangle =\frac{1}{\sqrt{2}}\left( |00\rangle -|11\rangle \right) ,|{\psi _2}^-\rangle =\frac{1}{\sqrt{2}}\left( |01\rangle -|10\rangle \right) $, we can check that \(\rho _3\) is always separable with PPT criterion.