Creation of superposition of unknown quantum states

TL;DR

This paper investigates the fundamental limits and possibilities of creating superpositions of unknown quantum states, proving a no-go theorem and providing an optimal probabilistic protocol for specific cases.

Contribution

It establishes a no-go theorem for universal superposition creation and introduces a unique, optimal protocol for states with fixed overlaps, applicable to arbitrary Hilbert spaces.

Findings

No universal probabilistic protocol exists for superposing two unknown states.

An explicit protocol is provided for states with fixed overlaps, proven to be optimal.

The protocol can be implemented in quantum optics to generate nonclassical states.

Abstract

The superposition principle is one of the landmarks of quantum mechanics. The importance of quantum superpositions provokes questions about the limitations that quantum mechanics itself imposes on the possibility of their generation. In this work we systematically study the problem of creation of superpositions of unknown quantum states. First, we prove a no-go theorem that forbids the existence of a universal probabilistic quantum protocol producing a superposition of two unknown quantum states. Secondly, we provide an explicit probabilistic protocol generating a superposition of two unknown states, each having a fixed overlap with the known referential pure state. The protocol is proven to be unique and optimal. Moreover, it can be implemented on arbitrary Hilbert spaces. In the context of quantum optics it can be used to efficiently generate highly nonclassical or nongaussian states.