Quantum mechanics dictates bounds for the minimal evolution time between predetermined initial and final states. Several of these Quantum Speed Limit (QSL) bounds were derived for non-unitary dynamics using different approaches. Here, we perform a systematic analysis of the most common QSL bounds in the damped Jaynes-Cummings model, covering the Markovian and non-Markovian regime. We show that only one of the analysed bounds cleaves to the essence of the QSL theory outlined in the pioneer works of Mandelstam & Tamm and Margolus & Levitin in the context of unitary evolutions. We also show that all of QSL bounds analysed reflect the fact that in our model non-Markovian effects speed up the quantum evolution. However, it is not possible to infer the Markovian or non-Markovian behaviour of the dynamics only analysing the QSL bounds. t , is, within the analysed QSL bounds, the only one that sticks close to the essence of the QSL theory. This essence is not to estimate the actual evolution arXiv:1609.04396v1 [quant-ph]

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. arXiv:1903.07489v1 [quant-ph]

The problem of quantum metrology in the context of a particular non-Markovian quantum evolution is explored. We study the dynamics of the quantum Fisher information (QFI) of a composite quantum probe coupled to a Lorentzian environment, for a full variety of different classes of parameters. We are able to find the best metrological state, which is not maximally entangled but is the one which evolves the most rapidly. This is shown by demonstrating a connection between QFI and different quantum speed limits. At the same time, by optimizing a control field acting on the probes, we show how the total information flow is actively manipulated by the control so as to enhance the parameter estimation at a given final evolution time. Finally, under this controlled scenario, a sharp interplay between the dynamics of QFI, non-Markovianity, and entanglement is revealed within different control schemes.

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It is widely spread in the literature that non-Markovianity (NM) may be regarded as a resource in quantum mechanics. However, it is still unclear how and when this alleged resource may be exploited. Here, we study the relationship between NM and quantum optimal control under the objective of generating entanglement within M non-interacting subsystems, each one coupled to the same non-Markovian environment. Thus, we design a variety of entangling protocols that are only achievable due to the existence of the environment. We show that NM plays a crucial role in all the entangling protocols considered, revealing that the degree of NM completely determines the success of the entangling operation performed by the control. This is a demonstration of the virtues of NM and the way that it can be exploited in a general entangling setup.