A geometrical description of the universal $1 \to 2$ asymmetric quantum cloning region

TL;DR

This paper characterizes the parameter space of universal 1 to 2 asymmetric quantum cloning using a geometric approach, revealing that the achievable region forms a union of ellipses and exploring negative singlet fractions.

Contribution

It introduces a geometric description of the cloning parameter region and extends the analysis to include negative singlet fractions, a novel aspect.

Findings

The achievable cloning parameters form a union of ellipses.

The parameter region corresponds to quantum state compatibility of isotropic states.

Negative singlet fractions are considered for the first time.

Abstract

We consider the problem of determining the achievable region of parameters for universal $1 \to 2$ asymmetric quantum cloning. Measuring the cloning performance with the figure of merit of singlet fraction, we show that the physical region is a union of ellipses in the plane. Equivalently, we characterize the parameter region of quantum state compatibility of two possibly different isotropic states, considering, for the first time, negative singlet fractions.