Distance Bounds on Quantum Dynamics

TL;DR

This paper establishes rigorous upper bounds on how far quantum states can diverge over time in open systems, based on the differences in their governing Hamiltonians, with practical implications for decoherence protection.

Contribution

It introduces new bounds relating quantum state divergence to Hamiltonian differences, applicable to open quantum systems and decoherence mitigation.

Findings

Derived explicit upper bounds on quantum state distances

Applied bounds to decoherence protection via dynamical decoupling

Demonstrated bounds' relevance in open quantum system control

Abstract

We derive rigorous upper bounds on the distance between quantum states in an open system setting, in terms of the operator norm between the Hamiltonians describing their evolution. We illustrate our results with an example taken from protection against decoherence using dynamical decoupling.