I am unable to find the solution to the following equation:
Tr$_{2}[U(|\psi\rangle \langle\psi|\otimes \rho)U^{\dagger}]=\rho$
Here $\psi$ is state vector representing a qubit and $\rho$ state of second qubit(the partial trace is over its subspace).
Also $U$ is a unitary operator given by $\sum |x \vee y\rangle |y\rangle \langle x| \langle y|$ where $x,y \in \{0,1\}$
$\vee$ stands for bit XOR and $\otimes$ for tensor product and $U$ operates on joint space of both the qubits.