Purification in Rapid Repeated Interaction Systems

TL;DR

This paper studies how rapid repeated quantum interactions can purify a system, providing necessary and sufficient conditions for purification and analyzing the role of interaction complexity in achieving effective purification.

Contribution

It introduces a precise criterion for purification in repeated interaction systems and characterizes the impact of interaction complexity on purification strength.

Findings

Purification occurs under specific conditions in repeated quantum interactions.

Simple tensor product interactions are ineffective for purification.

Complex interactions with a minimum degree of complexity enable stronger purification.

Abstract

We investigate the open dynamics of a quantum system when it is rapidly repeatedly updated by a quantum channel. Specifically, we analyze when this dynamics can purify the system. We develop a necessary and sufficient condition for such purification effects to occur and characterize their strength. We thoroughly analyze the specific scenario of a quantum system undergoing rapid unitary interactions with a sequence of ancillary quantum systems. We find that while the purification effects are generally present, in order for these effects to be strong compared to the decoherence effects the interaction Hamiltonian must have a minimum degree of complexity. Specifically, a tensor product interaction $\hat{Q}_\text{S}\otimes\hat{R}_\text{A}$, as well as many common light-matter interactions cannot purify efficiently.