Virtual Cloning of Quantum States

TL;DR

This paper introduces a virtual-cloning protocol that circumvents the quantum no-cloning theorem by using a simulation-based approach, providing a framework and bounds for cloning quantum states virtually.

Contribution

It proposes a novel virtual cloning method, formulates the problem as semidefinite programming, and links it to state discrimination to establish cloning cost bounds.

Findings

Derived a necessary and sufficient criterion for virtual cloning

Formulated the virtual cloning problem as semidefinite programming

Established universal bounds on cloning cost via state discrimination

Abstract

The inherent limitations of physical processes prevent the copying of arbitrary quantum states. Furthermore, even if we only aim to clone two distinct quantum states, it remains impossible unless they are mutually orthogonal. To overcome this limitation, we propose a virtual-cloning protocol that bypasses the restrictions imposed by the quantum no-cloning theorem. Specifically, we begin by outlining the general framework for virtual cloning and deriving a necessary and sufficient criterion for the existence of a virtual operation capable of simultaneously cloning a set of states. Subsequently, through an analysis of the simulation cost of the virtual-cloning process, we demonstrate that the problem of identifying an optimal virtual-cloning protocol can be cast as a semidefinite programming problem. Finally, we establish a connection between virtual cloning and state discrimination, from which universal bounds on the optimal cloning cost are derived.