Editing Probabilistic Cloning (section)

==Properties==
'''Success Probability Claims'''</br>
*'''General case:''' The success probability for cloning the elements of the input set of linearly independent states satisfies the following matrix relation:</br>
<math>X^{(1)} = \sqrt{P}X^{(2)}\sqrt{P^{\dagger}} + CC^{\dagger}</math></br></br>
where <math>\sqrt{P} = \sqrt{P^{\dagger}} = diag(\sqrt{p_1}, .... \sqrt{p_n})</math>,</br>
<math>X^{(k)} = \langle\psi_i|\psi_j\rangle^k</math>, </br>
and <math>C = [c_{ij}]</math>
*'''Two qubits case:''' The optimal success probability for the probabilistic machine which is able to clone two non-orthogonal qubits is:</br>
<math>p = \frac{1}{1 + cos2\eta}</math>