  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.
