Abstract
We investigate the conditions under which an uncontrollable background processes may be harnessed by an agent to perform a task that would otherwise be impossible within their operational framework. This situation can be understood from the perspective of resource theory: rather than harnessing 'useful' quantum states to perform tasks, we propose a resource theory of quantum processes across multiple points in time. Uncontrollable background processes fulfil the role of resources, and a new set of objects called superprocesses, corresponding to operationally implementable control of the system undergoing the process, constitute the transformations between them. After formally introducing a framework for deriving resource theories of multi-time processes, we present a hierarchy of examples induced by restricting quantum or classical communication within the superprocess — corresponding to a client-server scenario. The resulting nine resource theories have different notions of quantum or classical memory as the determinant of their utility. Furthermore, one of these theories has a strict correspondence between non-useful processes and those that are Markovian and, therefore, could be said to be a true 'quantum resource theory of non-Markovianity'.
Highlights
Before the invention of motors powered by hydrocarbon fuel, our ancestors were forced to rely on less tangible energy sources to power their voyages across the oceans
Fast forward a few hundred years, and we are at the cusp of another technological revolution, which will be based on the logic of quantum mechanics
We can construct a meaningful resource theory of multi-time quantum processes by placing restrictions on an agent’s control: The control sequences which the agent is capable of performing correspond to a set of superprocesses that relate them to a fiducial set of control sequences on s
Summary
Before the invention of motors powered by hydrocarbon fuel, our ancestors were forced to rely on less tangible energy sources to power their voyages across the oceans. A wind turbine (solar panel) is useless on windless sunny (stormy) day This example begs the question: under what conditions is it possible to extract useful work or information out of an uncontrolled background quantum process?. Stabiliser computation, magic states are useful [15] These resource theories do not capture the usefulness of more general quantum processes, which take place over several points in time and which may involve temporal correlations mediated by an inaccessible environment i.e., non-Markovian memory. It appears that non-Markovianity is the norm rather than the exception; it must be accounted for in real quantum computers [16], in quantum metrology with noisy environments [17], and in many realistic quantum control tasks [18]. We will elucidate the general scenario we have in mind
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