Non-Markovian quantum control as coherent stochastic trajectories

TL;DR

This paper introduces a framework for stochastic quantum trajectories, distinguishing between entanglement-breaking and coherent processes, and demonstrates how non-Markovianity can be harnessed as a quantum resource through coherent control.

Contribution

It develops a basis of elementary trajectories for non-Markovian quantum processes and shows how coherent trajectories can be used to turn non-Markovianity into a resource.

Findings

Non-Markovian processes can be decomposed into elementary trajectories.

Coherent trajectories enable decoupling from the environment while preserving quantum information.

Non-Markovianity involves more quantum than classical correlations.

Abstract

We develop a notion of stochastic quantum trajectories. First, we construct a basis set of trajectories, called elementary trajectories, and go on to show that any quantum dynamical process, including those that are non-Markovian, can be expressed as a linear combination of this set. We then show that the set of processes divide into two natural classes: those that can be expressed as convex mixture of elementary trajectories and those that cannot be. The former are shown to be entanglement breaking processes (in each step), while the latter are dubbed coherent processes. This division of processes is analogous to separable and entangled states. In the second half of the paper, we show, with an information theoretic game, that when a process is non-Markovian, coherent trajectories allow for decoupling from the environment while preserving arbitrary quantum information encoded into the system. We give explicit expressions for the temporal correlations (quantifying non-Markovianity) and show that, in general, there are more quantum correlations than classical ones. This shows that non-Markovian quantum processes are indeed fundamentally different from their classical counterparts. Furthermore, we demonstrate how coherent trajectories (with the aid of coherent control) could turn non-Markovianity into a resource. In the final section of the paper we explore this phenomenon in a geometric picture with a convenient set of basis trajectories.