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Universal Quantum Cloning
Universal quantum cloning (UQC) implies that the quality of the output (cloned state) is not dependent on the input, thus the process is "universal" to any input state. The output state produced is governed by the Hamiltonian of the system.

One of the first cloning machines, a 1 to 2 UQC machine, was proposed in 1996 by Buzek and Hillery. As the name implies, the machine produces two identical copies of a single input qubit with a fidelity of 5/6 when comparing only one output qubit, and global fidelity of 2/3 when comparing both qubits. This idea was expanded to more general cases such as an arbitrary number of inputs and copies, as well as d-dimensional systems.

Multiple experiments have been conducted to realize this type of cloning machine physically by using photon stimulated emission. The concept relies on the property of certain three-level atoms to emit photons of any polarization with equally likely probability. This symmetry ensures the universality of the machine.

Phase Covariant Cloning
When input states are restricted to Bloch vectors corresponding to points on the equator of the Bloch Sphere, more information is known about them. The resulting clones are thus state-dependent, having an optimal fidelity of $1/2 + \sqrt(1/8) \approx 0.8536$. Although only having a fidelity slightly greater than the UQCM (~0.83), phase covariant cloning has the added benefit of being easily implemented through quantum logic gates consisting of the rotational operator $\hat{R}(\vartheta)$ and the controlled-NOT (CNOT). Output states are also separable according to Peres-Horodecki criterion.

The process has been generalized to the 1 → M case and proven optimal. This has also been extended to the qutrit and qudit cases. The first experimental asymmetric quantum cloning machine was realized in 2004 using nuclear magnetic resonance.

Asymmetric Quantum Cloning
The first family of asymmetric quantum cloning machines was proposed by Nicholas Cerf in 1998. A cloning operation is said to be asymmetric if its clones have different qualities and are all independent of the input state. This is a more general case of the symmetric cloning operations discussed above which produce identical clones with the same fidelity. Take the case of a simple 1 → 2 asymmetric cloning machine. There is a natural trade-off in the the cloning process in that if one clone's fidelity is fixed to a higher value, the other must decrease in quality and vice versa. The optimal trade off is bounded by the following inequality :

$$(1-F_d)(1-F_e)\geq[1/2-(1-F_d)-(1-F_e)]^2$$ where Fd and Fe are the state-independent fidelities of the two copies.

This type of cloning procedure was proven mathematically to be optimal as derived from the Choi-Jamiolkowski channel state duality. However, even with this cloning machine perfect quantum cloning is proved to be unattainable.

Probabilistic Quantum Cloning
In 1998, Duan and Guo proposed a different approach to quantum cloning machines that relies on probability. This machine allows for the perfect copying of quantum states without violation of the No-Cloning and No-Broadcasting Theorems, but at the cost of not being 100% reproducible. The cloning machine is termed "probabilistic" because it performs measurements in addition to a unitary evolution. These measurements are then sorted through to obtain the perfect copies with a certain quantum efficiency (probability). As only orthogonal states can be cloned perfectly, this technique can be used to identify non-orthogonal states. The process is optimal when $\eta=1/(1+|\langle\Psi_0|\Psi_1\rangle)$  where η is the probability of success for the states Ψ0 and Ψ1.

The process was proven mathematically to clone two pure, non-orthogonal input states using a unitary-reduction process. One implementation of this machine was realized through the use of a "noiseless optical amplifier" with a success rate of about 5%.