Universal superposition of arbitrary orthogonal states

TL;DR

This paper introduces universal quantum machines capable of creating superpositions of unknown orthogonal states with certainty, revealing a fundamental link between no-cloning and no-superposition principles in quantum mechanics.

Contribution

It demonstrates the existence of universal superposition machines for orthogonal states, establishing a connection between cloning and superposition theorems.

Findings

Universal machines can produce superpositions of orthogonal states with 100% success.

The existence of perfect cloning implies the possibility of universal superposition machines.

The work clarifies the relationship between no-cloning and no-superposition theorems in quantum theory.

Abstract

It is known that no quantum process can produce a predetermined superposition of unknown arbitrary states. It has already been shown that with some partial information about the states, one can produce with some probability such superpositions. Here we show that there are universal machines which can produce superpositions of unknown orthogonal states with unit probability. Our construction unravels the relation between the no-cloning theorem and the no-superposition theorem, that is we show that if a perfect cloning machine exists, then a universal superposition machine can also exist.