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

## TL;DR

This paper develops a resource theory framework for multi-time quantum processes, revealing how uncontrollable background processes can serve as resources, and identifies a specific theory that characterizes quantum non-Markovianity as a resource.

## Contribution

It introduces a formal resource theory of multi-time quantum processes, including superprocesses and a hierarchy of theories based on communication restrictions, highlighting non-Markovianity as a quantum resource.

## Key findings

- Nine distinct resource theories based on communication constraints.
- Identification of a theory where non-Markovian processes are resources.
- A formal framework connecting uncontrollable processes and quantum memory.

## 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'.