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

TL;DR

This paper develops an optimal quantum cloning machine for qubits with arbitrary axisymmetric distributions on the Bloch sphere, generalizing phase-covariant cloning to a broader class of input states with analytical fidelity expressions.

Contribution

It introduces a new class of optimal cloning machines for axisymmetric distributions, extending phase-independent cloning with analytical formulas and implementation methods.

Findings

Derived analytical expressions for cloning fidelity.

Analyzed cloning of von Mises-Fisher and Brosseau distributions.

Proposed implementation via modified mirror phase-covariant cloning machine.

Abstract

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 analytical 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.