Consider the state (left|chi_{1,2}^{a} ightangle=left|psi_{1,2} ightangle+aleft|phi_{1,2} ightangle), for an arbitrary (a in mathbb{R}). When is it separable?

Consider the state \(\left|\chi_{1,2}^{a}\rightangle=\left|\psi_{1,2}\rightangle+a\left|\phi_{1,2}\rightangle\), for an arbitrary \(a \in \mathbb{R}\). When is it separable? Calculate \(ho_{A}\) and \(ho_{B}\) to check that you find the correct results.