Optimal cloning with respect to the relative error

TL;DR

This paper investigates the limits of quantum state cloning based on relative error, deriving bounds, analyzing specific cases, and constructing circuits for optimal cloning of pure states.

Contribution

It introduces a new lower bound on the relative error for quantum cloning considering prior information and provides a quantum circuit for optimal cloning of two pure states.

Findings

Derived the lower bound on relative error for quantum cloning.

Analyzed cloning scenarios for two-state and multi-state sets.

Constructed a quantum circuit for optimal cloning of two pure states.

Abstract

The relative error of cloning of quantum states with arbitrary prior probabilities is considered. It is assumed that the ancilla may contain some a priori information about the input state to be cloned. The lower bound on the relative error for general cloning scenario is derived. Both the case of two-state set and case of multi-state set are analyzed in details. The treated figure of merit is compared with other optimality criteria. The quantum circuit for optimal cloning of a pair of pure states is constructed.