Given a pure two qubit state $|\psi_{AB}\rangle$. If we trace out system $B$, the remaining density matrix $\rho_A = Tr_B|\psi_{AB}\rangle\langle\psi_{AB}|$, can be represented as a point lying anywhere on or inside a Blochsphere.
When you're on the Bloch sphere you have a separable state; when you're in the center, your state is maximally entangled. So by entanglement you can affect the distance from the center.
How do have to steer (by applying timevarying unitaries $U(t)$) the composite system $|\psi_{AB}\rangle$, such that the resulting trajectory on or inside the Bloch sphere of system $A$ is an ellipse? $$ \rho_A(t)=Tr_B \left( U(t)|\psi_{AB}\rangle\langle\psi_{AB}|U'(t)\right) \sim\pmatrix{x(t)\\y(t)\\z(t)}_{\text{Bloch}_A} \text{ with } \frac{x^2(t)}{a^2}+\frac{y^2(t)}{b^2}=1 $$
