title: Creating a Superposition of Unknown Quantum 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 the 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. Second, 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 can be applied to generate coherent superposition of results of independent runs of subroutines in a quantum computer. Moreover, in the context of quantum optics it can be used to efficiently generate highly nonclassical states or non-Gaussian states.
authors.affiliation: Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland and ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain.
authors.forename: Michał
authors.initials: M
authors.lastname: Oszmaniec
authors.affiliation: Faculty of Physics, Adam Mickiewicz University, 61-614 Poznan, Poland.
authors.forename: Andrzej
authors.initials: A
authors.lastname: Grudka
authors.affiliation: Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-952 Gdańsk, Poland and Institute of Theoretical Physics and Astrophysics, and National Quantum Information Centre in Gdańsk, 81-824 Sopot, Poland.
authors.forename: Michał
authors.initials: M
authors.lastname: Horodecki
authors.affiliation: Faculty of Physics, Adam Mickiewicz University, 61-614 Poznan, Poland.
authors.forename: Antoni
authors.initials: A
authors.lastname: Wójcik