Quantum mechanics

Theoretical physics

Process (computing)

Statistics

Markov process

Materials science

Coherence (philosophical gambling strategy)

Quantum process

Operating system

Range (aeronautics)

Set (abstract data type)

Computer science

Observable

Statistical physics

Physics

Database

Quantum dynamics

Mathematics

Geometry

Quantum

Composite material

Connection (principal bundle)

Measure (data warehouse)

Quantum discord

Programming language

Open quantum system

Physical Review X

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.

When Is a Non-Markovian Quantum Process Classical?