Optimal Universal Quantum Cloning: Asymmetries and Fidelity Measures

TL;DR

This paper investigates the limits of universal quantum cloning, focusing on fidelity trade-offs and asymmetries, providing a comprehensive formalism and extending known results on optimal cloning machines.

Contribution

It introduces a quadratic constraint framework for analyzing quantum cloning, reproduces existing results, and advances the understanding of asymmetric cloning fidelity trade-offs.

Findings

Derived new trade-off relations for asymmetric cloning fidelities

Reproduced all known results on optimal universal cloning

Provided evidence on limitations for other parameter ranges

Abstract

We study the problem of universal quantum cloning -- taking several identical copies of a pure but unknown quantum state and producing further copies. While it is well known that it is impossible to perfectly reproduce the state, how well the copies can be cloned can be quantified using the fidelity. We examine how individual fidelities can be traded against each other, and how different fidelity measures can be incorporated. The broadly applicable formalism into which we transform the cloning problem is described as a series of quadratic constraints which are amenable to mathematical and computational scrutiny. As such, we reproduce all known results on optimal universal cloning, and push the recent results on asymmetric cloning much further, giving new trade-off relations between fidelities for broad classes of optimal cloning machines. We also provide substantial evidence that motivates why other parameter ranges (number of input copies) have not, and will not, yield to similar analysis.