Optimal cloning of qubits given by an arbitrary axisymmetric distribution on the Bloch sphere

Karol Bartkiewicz, Adam Miranowicz
2010 Physical Review A. Atomic, Molecular, and Optical Physics  
We find an optimal quantum cloning machine, which clones qubits of arbitrary symmetrical distribution around the Bloch vector with the highest fidelity. The process is referred to as phase-independent cloning in contrast to the standard phase-covariant cloning for which an input qubit state is a priori better known. We assume that the information about the input state is encoded in an arbitrary axisymmetric distribution (phase function) on the Bloch sphere of the cloned qubits. We find
more » ... l expressions describing the optimal cloning transformation and fidelity of the clones. As an illustration, we analyze cloning of qubit state described by the von Mises-Fisher and Brosseau distributions. Moreover, we show that the optimal phase-independent cloning machine can be implemented by modifying the mirror phase-covariant cloning machine for which quantum circuits are known.
doi:10.1103/physreva.82.042330 fatcat:y2licxeekneffalilj3lzcckae