A continuous-time diffusion limit theorem for dynamical decoupling and intrinsic decoherence

TL;DR

This paper analyzes the mathematical foundations of random dynamical decoupling in quantum systems, deriving analytical expressions for system evolution and demonstrating its limitations against intrinsic decoherence.

Contribution

It provides a rigorous mathematical framework for understanding dynamical decoupling, including limit theorems and explicit formulas for quantum state evolution.

Findings

Delineates the continuum-time limit behavior of dynamical decoupling

Provides explicit formulas for expectation and variance of quantum states

Shows dynamical decoupling fails against intrinsic decoherence

Abstract

We discuss a few mathematical aspects of random dynamical decoupling, a key tool procedure in quantum information theory. In particular, we place it in the context of discrete stochastic processes, limit theorems and CPT semigroups on matrix algebras. We obtain precise analytical expressions for expectation and variance of the density matrix and fidelity over time in the continuum-time limit depending on the system Lindbladian, which then lead to rough short-time estimates depending only on certain coupling strengths. We prove that dynamical decoupling does not work in the case of intrinsic (i.e., not environment-induced) decoherence, and together with the above-mentioned estimates this yields a novel method of partially identifying intrinsic decoherence.