A question about the universal quantum cloning machine (UQCM)

In the recent paper Replicating the benefits of Deutschian closed timelike curves without breaking causality, a quantum state cloner based on open timelike curve (OTC) was mentioned.

There to clone a $d$-dimensional state $\rho$, the first step is to make $O(d^2)$ identical imperfect clones $\rho'$ of the state to be cloned by UQCM. Then these imperfect clones $\rho'$ were duplicated by OTC to get measured by an information complete measurement set to estimate the density matrix $\rho'$, then based on the estimation of the density matrix of $\rho'$, $\rho$ can be reconstructed to achieve the cloning of $\rho$.

My question is: It seems that the UQCM can only work on qudit and so no entanglement is involved (Maybe I am wrong about this). IF what I want to clone is an entangled state with a density matrix $\rho_{AB}$, does such kind of UQCM also work so that it can produce multiple imperfect copies of $\rho_{AB}$ in a well controlled way as it works on qudits?

Or an alternative way, for an entangled qubit pair $\psi_{AB}=a|00>+b|01>+c|10>+d|11>$, can we accordingly generate a qudit in $\phi_D=a|x_0>+b|x_1>+c|x_2>+d|x_3>$ with $\{x_i\}$ orthogonal states so that the state of $\psi_{AB}$ can be cloned by applying the OTC based strategy on qudit $D$ to estimate $\phi_D$?

Maybe it's just a stupid question. Please correct me if I am totally wrong.

• I've deleted an unconstructive comment discussion. – David Z Jan 3 '16 at 13:24