Can someone help in applying covariance condition to this unitary transformation?

I am trying to apply covariance property on this Quantum adder transformation in which a two particle input state is mapped onto a two particle output state. I am trying to represent these states into a bloch sphere density operator and apply the covariance condition to the same. I don't know how to work around the same.

$$U \lvert\Psi_1 \rangle\lvert \Psi_2 \rangle \propto \left( \lvert \Psi_1 \rangle + \lvert \Psi_2 \rangle \right) \lvert \chi \rangle$$

• what do you mean with "covariance property"? Can you add some context and references? – glS Sep 23 at 12:42
• @glS You can get to know about the covariance condition here in this paper : (arxiv.org/pdf/quant-ph/9801005.pdf) – GRAND GRV Sep 24 at 4:27