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The extraction of work (i.e., usable energy) from quantum processes is a key focus of quantum thermodynamics research, which explores the application of thermodynamics laws to quantum systems. Meanwhile, other quantum physics research has been investigating the non-Markovian dynamics of open quantum systems, which entail the influence of past states on the systems' future evolution.

Researchers at the University of Nottingham and University of São Paulo have introduced a general and rigorous framework that bridges quantum thermodynamics and non-Markovian dynamics, showing that the latter could serve as a resource that can be exploited to enhance the extraction of work from quantum processes.

Their paper, in ÌÇÐÄÊÓƵical Review Letters, could open new possibilities for the future development of quantum technologies.

"This paper came about when the lead author, Guilherme Zambon, a Ph.D. student from São Paulo, got funding from FAPESP to visit my group at Nottingham for one year," Gerardo Adesso, co-author of the paper, told ÌÇÐÄÊÓƵ.

"We were inspired by early characterizations of thermodynamics as a resource theory, and our initial objective was to extend such studies to characterize work extraction from general multi-time quantum processes, not just states or channels."

The recent study by Adesso and Zambon was aimed at bridging two rapidly evolving areas of quantum information science, which have so far been mostly considered individually. The first area is quantum thermodynamics, studied through the lens of resource theory, while the second is non-Markovianity, analyzed in the context of the so-called process tensor framework.

"While it was broadly understood that memory effects could enhance thermodynamic processes, a general and rigorous connection between these concepts was still missing," said Zambon, co-author of the paper. "Our primary objective was to establish this link, providing a unified perspective on how memory influences quantum thermodynamic tasks."

While trying to connect quantum thermodynamics and non-Markovian dynamics, the researchers realized that there is more than one way of extracting work from general quantum processes. They ultimately identified four distinct strategies and found that they could be naturally arranged into a hierarchical structure, based on the overall efficiency with which they enabled the extraction of work from quantum processes.

"We realized quite soon that for Markovian processes the whole hierarchy collapses, meaning that the most elaborate strategies do not offer any advantage for work extraction, and the best one could do is a sequential procedure of extracting work independently from each step of the process," explained Adesso.

"However, in general non-Markovian processes, the hierarchy becomes strict, and we revealed definite advantages at every step. Interestingly, we could pin these down to specific features of non-Markovianity, such as memory effects and temporal correlations. We have specific examples illustrating these for each layer in our hierarchy."

In their paper, Adesso and Zambon represent general quantum processes as "quantum combs," mathematical structures that can be used to describe multi-step quantum processes. Their proposed framework then adopts a well-known quantum thermodynamics theory, known as the resource theory of thermal operations, to estimate the work extractable from quantum processes.

"Work is quantified in terms of free energy, and non-Markovianity is quantified via a geometric measure defined on the combs (which was previously introduced by Zambon)," explained Adesso.

"Our connection is not only qualitative, but quantitative: climbing up the hierarchy, the extra work which can be extracted is precisely limited by the amount of non-Markovianity of the process. The most interesting result for me is the hierarchy of work extraction strategies enabled by non-Markovianity."

The new framework introduced by Adesso and Zambon is both mathematically elegant and insightful, as it shows that non-Markovianity offers various fundamental advantages in terms of quantum thermodynamics. In addition to advancing the understanding of quantum systems, the framework could inform the future development of technologies that rely on quantum thermodynamic processes.

"Our key contribution was establishing a rigorous and general relationship between thermodynamics and memory effects, clarifying the mechanisms that enable enhanced work extraction in non-Markovian processes," said Zambon.

"Additionally, we derived continuity bounds that quantify how much advantage can be gained depending on the degree of non-Markovianity—a step toward practical applications. These findings could influence the design of quantum thermal machines, batteries, and even inform the thermodynamic costs of quantum computation."

The researchers hope that the theoretical framework they devised will soon contribute to the advancement of various quantum technologies.

While the results of their recent study specifically apply to processes with a definite arrow of time, they now plan to determine whether an indefinite causal order can also serve as a resource for work extraction.

"More fundamentally, we are keen to research whether our best strategy for work extraction from quantum combs is reversible, i.e. whether by spending as much work (and not more) one could implement the process back by means of thermal operations," said Adesso.

"We are also keen to explore experimental demonstrations, possibly with nuclear magnetic resonance setups, and analyze naturally occurring non-Markovian processes and their thermodynamical efficiency; this can shed new light on the increasingly popular interface between quantum information and biochemical sciences."

As part of their future research, Adesso and Zambon will also explore the practical applications of their new theoretical framework. For instance, they would like to use it to study the processes underpinning the functioning of quantum batteries, focusing on how memory effects can optimize the storage and extraction of energy.

"We also plan to use our framework to study the thermodynamics of computation, or in other words, energetic trade-offs in quantum information processing," added Zambon.

"Moving forward, we plan to explore these results in more concrete settings. By focusing on these specific scenarios, we hope to uncover new insights with direct experimental relevance."

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