  The issue of whether non-Markovianity (NM) could be considered as a resource
in quantum information has been a subject of intense debate for the last years.
Recently, a simple mechanism was proposed in which one of the main features of
NM, the backflow of information from the environment to the system, represents
a fundamental and quantifiable resource for generating entanglement within an
open quantum system coupled to a finite and small environment [N. Mirkin, P.
Poggi and D. Wisniacki, Phys. Rev. A, 99(2), 020301(R)]. In this work, we
extend the universality of this resource mechanism by studying a completely
different and more general scheme where the system is coupled to an infinite
structured reservoir. Under both setups, we show that the degree of NM
univocally determines the optimal degree of entanglement reachable by
controlling the open system. This result reveals the universality of a
quantitative relation between entanglement and NM by using quantum optimal
control.
