Resource theories of multi-time processes: A window into quantum non-Markovianity. (arXiv:1907.07003v1 [quant-ph])

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'.

Article web page: