Almost Markovian processes from closed dynamics

TL;DR

This paper proves that quantum processes involving small subsystems of large closed systems are almost Markovian with high probability, providing foundational insights into quantum dynamics without common approximations.

Contribution

It introduces a formal proof that small subsystems of large closed quantum systems are nearly Markovian, without relying on weak coupling or other typical assumptions.

Findings

Processes are close to Markovian with high probability as system size increases.

Non-Markovian effects may be significant over long times for fixed system sizes.

Detecting non-Markovianity requires non-trivial entangling resources.

Abstract

It is common, when dealing with quantum processes involving a subsystem of a much larger composite closed system, to treat them as effectively memory-less (Markovian). While open systems theory tells us that non-Markovian processes should be the norm, the ubiquity of Markovian processes is undeniable. Here, without resorting to the Born-Markov assumption of weak coupling or making any approximations, we formally prove that processes are close to Markovian ones, when the subsystem is sufficiently small compared to the remainder of the composite, with a probability that tends to unity exponentially in the size of the latter. We also show that, for a fixed global system size, it may not be possible to neglect non-Markovian effects when the process is allowed to continue for long enough. However, detecting non-Markovianity for such processes would usually require non-trivial entangling resources. Our results have foundational importance, as they give birth to almost Markovian processes from composite closed dynamics, and to obtain them we introduce a new notion of equilibration that is far stronger than the conventional one and show that this stronger equilibration is attained.