# When is a non-Markovian quantum process classical?

## TL;DR

This paper characterizes when non-Markovian quantum processes can be considered classical, showing that memory effects do not necessarily imply non-classicality and providing measures to identify genuinely quantum processes.

## Contribution

It offers a full characterization of classical processes in non-Markovian quantum systems and links classicality to quantum discord, highlighting genuinely quantum phenomena with memory.

## Key findings

- Classical processes can be fully characterized in non-Markovian quantum systems.
- Absence of coherence does not imply classicality in processes with memory.
- Existence of genuinely quantum non-Markovian processes independent of measurement schemes.

## Abstract

More than a century after the inception of quantum theory, the question of which traits and phenomena are fundamentally quantum remains under debate. Here we give an answer to this question for temporal processes which are probed sequentially by means of projective measurements of the same observable. Defining classical processes as those that can---in principle---be simulated by means of classical resources only, we fully characterize the set of such processes. Based on this characterization, we show that for non-Markovian processes (i.e., processes with memory), the absence of coherence does not guarantee the classicality of observed phenomena and furthermore derive an experimentally and computationally accessible measure for non-classicality in the presence of memory. We then provide a direct connection between classicality and the vanishing of quantum discord between the evolving system and its environment. Finally, we demonstrate that---in contrast to the memoryless setting---in the non-Markovian case, there exist processes that are genuinely quantum, i.e., they display non-classical statistics independent of the measurement scheme that is employed to probe them.