Information backflow as a resource for entanglement

The issue of whether non-Markovianity (NM) could be considered as a resource in quantum information has been a subject of intense debate in recent 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, 020301(R) (2019)]. In this work, we extend the validity 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 strongly suggests the universality of a quantitative relation between entanglement and NM by using quantum optimal control.

Figure 1

The three different entangling protocols considered under non-Markovian dynamics. (a) Single addressing (SA): we can just access and control one of the systems. (b) Double addressing (DA): we control both systems with different fields. (c) Global addressing (GA): the same field is simultaneously controlling both of the systems.

Figure 2

Optimal entanglement obtained as a function of the original degree of NM for the case of single addressing (SA), double addressing (DA), and global addressing (GA). In the upper panel driving time is fixed as $T=1$, while in the lower panel $T=4$ ($\hslash =1$ and in units of $1/{\omega }_0$). Each point represents a physical situation in which random coupling constants ${\alpha }_1$ and ${\alpha }_2$ are chosen within the intervals $0<{\alpha }_1<1/\sqrt{2}$ and $0<{\alpha }_2<0.2$. Just points inside the interval ${10}^{-6}<\mathcal{N}<0.3$ are shown, while points with $\mathcal{N}<{10}^{-6}$ were excluded in the plot for being considered inside the Markovian regime. For further discussion about the Markovian regime, see main text and Fig. 3.

Figure 3

Concurrence as a function of the original degree of NM in the case without control (yellow stars) and considering control under the single addressing method (black dots). Both Markovian and non-Markovian regions are shown for the same set of random couplings used in Fig. 2. The Markovian regime is highlighted with a grey area. Driving time is $T=1$ ($\hslash =1$ and in units of $1/{\omega }_0$).

Figure 4

Concurrence as a function of the original degree of NM in the case of single addressing (SA), double addressing (DA), and global addressing (GA). Each point represents a dynamics in which the coupling constants are chosen randomly in the interval $0\le A\le 0.2$, the total number of spins is also arbitrarily chosen within $2\le N\le 8$ and the driving time is fixed in $T=10$ ($\hslash =1$ and in units of $1/{\omega }_0$). On the other hand, in the inset we show the concurrence as a function of the original degree of NM in the case without control (yellow stars) and considering control under the single addressing method (black dots). The parameters in the inset are the same as in the main plot.