Resource theories of multi-time processes: A window into quantum non-Markovianity

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'.

Non-Markovian quantum dynamics: What does it mean?

“…For applications and experiments, see the accompanying Perspective article [31] The emphasis of the research seems to be turning from developing more definitions and quantifiers for non-Markovianity to understanding memory effects as a resource and how to combine the control of complex quantum systems with exploitation of memory effects. Indeed, discussion on full resource theory of non-Markovianity has began [63,64], though not yet completed in similar manner as has been achieved in a number of other fields of quantum physics or concepts therein.…”

Resource Preservability

“…Notably, resource theories for quantum channels (i.e. completelypositive trace-preserving maps [12]) and related topics have drawn much attention recently [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59].…”

Quantum metrology in a non-Markovian quantum evolution

“…In summary, regarding QFI has a clear practical meaning and that there is no discussion with respect whether it is useful or not for specific tasks (i.e. for quantum metrology), this result linking QFI and NM gives the last a clear and indisputable meaning as a quantum resource, either for estimating a parameter of the environment or even to maximally preserve the information of a parameter characterizing the reduced open system [25,26,[48][49][50][51] 2 .…”