Maximum possible fidelity in $1\rightarrow 2$ qubits cloning

TL;DR

This paper re-analyzes quantum cloning protocols to identify the maximum achievable fidelity in 1-to-2 qubit cloning, introduces a new state-dependent cloning method, and reports improved fidelity and entropy results.

Contribution

It demonstrates that the Bužek-Hillery protocol attains the maximum fidelity and introduces a novel state-dependent cloning protocol with higher fidelity.

Findings

Maximum fidelity matches phase covariant cloning results

New cloning protocol achieves fidelity of 0.847

Associated von-Neumann entropy is 0.825

Abstract

We re-analyse the Bu\v{z}ek-Hillery Universal Quantum Cloning machine protocol and show that it allows better values for fidelity and Hilbert-Schmidt norm than hitherto reported. This higher value for the fidelity is identical to the maximum fidelity of phase covariant quantum cloning of Bru\ss -Cinchetti-D'Ariano-Macchiavello. This value of fidelity has also been obtained by Niu and Griffiths in their work without machine states. This is the maximum possible fidelity obtainable in $1\rightarrow 2$ qubits cloning. We then describe a different and new state dependent cloning protocol with four machine states where all non-exact copies of input states are taken into account in the output and we use the Hessian method of determining extrema of multivariate functions. The fidelity for the best overall quantum cloning in this protocol is $\bar{F}=0.847$ with an associated von-Neumann entropy of $\bar{S}=0.825$.