Extremal asymmetric universal cloning machines

TL;DR

This paper explores the limits of asymmetric universal cloning machines, identifying extremal configurations that optimize output fidelities and trade-offs in quantum state replication.

Contribution

It characterizes all optimal output fidelities for 1 to 3 asymmetric cloning and constructs a family of extremal machines including symmetric and asymmetric cases.

Findings

Identified all attainable optimal output fidelities for 1 to 3 asymmetric cloning.

Discovered two types of extremal asymmetric cloning machines that cooperate to achieve optimal fidelities.

Constructed a family of extremal cloning machines including symmetric and asymmetric cases with optimal trade-offs.

Abstract

The trade-offs among various output fidelities of asymmetric universal cloning machines are investigated. First we find out all the attainable optimal output fidelities for the 1 to 3 asymmetric universal cloning machine and it turns out that there are two kinds of extremal asymmetric cloning machines which have to cooperate in order to achieve some of the optimal output fidelities. Second we construct a family of extremal cloning machines that includes the universal symmetric cloning machine as well as an asymmetric 1 to $1+N$ cloning machine for qudits with two different output fidelities such that the optimal trade-off between the measurement disturbance and state estimation is attained in the limit of infinite $N$.