Editing Phase Co-variant Cloning (section)

==Outline==
Phase Variant cloner can act effectively only on states lying on the equator of Bloch sphere. These states can be described by an angle factor such as <math>\phi</math> and aim of this protocol is to produce optimal copies of these states such that the fidelity of the copies in independent of <math>\phi</math>. This task can be done with two types of protocol: without any ancilla (test states) and with ancilla. Both methods produce copies with same optimal fidelity.
	
===Phase-covariant cloning without ancilla===
In this case a unitary transformation acts on two input states (the original state and a blank state) and produces a two-qubit state where the subsystem of each of the copies can be extracted from it. The unitary transformation depends on the shrinking factor but not on the phase. This unitary in general acts asymmetrically but it becomes a symmetric case when shrinking factor is equal to <math>\pi/4</math>.	
===Phase-covariant cloning with ancilla===
In this case, the transformation acts on three qubits (the original state and a 2-quit ancilla). The protocol is done in three steps:

# Prepare a Bell state <math>|\Phi^{+}\rangle</math>   
# Perform a 3-qubit unitary
# Discard the extra state
The fidelity of this protocol is the same as the previous protocol. However, the output states (reduced [[density matrices]] of copies) are different.