  We analyze various scenarios for entangling two initially unentangled qubits.
In particular, we propose an optimal universal entangler which entangles a
qubit in unknown state $|\Psi>$ with a qubit in a reference (known) state
$|0>$. That is, our entangler generates the output state which is as close as
possible to the pure (symmetrized) state $(|\Psi>|0> +|0>|\Psi>)$. The most
attractive feature of this entangling machine, is that the fidelity of its
performance (i.e. the distance between the output and the ideally entangled --
symmetrized state) does not depend on the input and takes the constant value
$F= (9+3\sqrt{2})/14\simeq 0.946$. We also analyze how to optimally generate
from a single qubit initially prepared in an unknown state $|\Psi\r$ a two
qubit entangled system which is as close as possible to a Bell state
$(|\Psi\r|\Psi^\perp\r+|\Psi^\perp\r|\Psi\r)$, where $\l\Psi|\Psi^\perp\r =0$.
