Unification of Random Dynamical Decoupling and the Quantum Zeno Effect

TL;DR

This paper unifies random dynamical decoupling with the quantum Zeno effect by analyzing average behaviors, showing that random decoupling protocols can induce quantum Zeno dynamics and lead to unitary bath evolution.

Contribution

It establishes a theoretical framework connecting random dynamical decoupling with the quantum Zeno effect, extending previous unification results to the random case.

Findings

Random dynamical decoupling converges to quantum Zeno dynamics.

The system's evolution approaches a unitary with a specific decoupling error.

A new framework called equitability of system and bath is introduced.

Abstract

Periodic deterministic bang-bang dynamical decoupling and the quantum Zeno effect are known to emerge from the same physical mechanism. Both concepts are based on cycles of strong and frequent kicks provoking a subdivision of the Hilbert space into independent subspaces. However, previous unification results do not capture the case of random bang-bang dynamical decoupling, which can be advantageous to the deterministic case but has an inherently acyclic structure. Here, we establish a correspondence between random dynamical decoupling and the quantum Zeno effect by investigating the average over random decoupling evolutions. This protocol is a manifestation of the quantum Zeno dynamics and leads to a unitary bath evolution. By providing a framework that we call equitability of system and bath, we show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.