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===Phase-covariant cloning without ancilla=== | ===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 | 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=== | ===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: | In this case, the transformation acts on three qubits (the original state and a 2-quit ancilla). The protocol is done in three steps: |