Quantum information spreading in inhomogeneous spin ensembles

TL;DR

This paper introduces a Krylov space framework to model quantum information spreading in inhomogeneous spin ensembles, revealing how frequency distributions influence information flow speed.

Contribution

It develops an exact theoretical approach for large spin ensembles, linking frequency distributions to quantum information dynamics and limits.

Findings

Derived exact expressions for Lieb-Robinson velocity and quantum speed limit.

Showed strong dependence of information flow speed on frequency distribution.

Implications for designing quantum technology components.

Abstract

We present a Krylov space based theoretical framework for modeling inhomogeneous spin ensembles with arbitrary distributions of spin frequencies and couplings. The framework is then used to asymptotically large spin ensemble. In the single-excitation subspace, the Krylov construction allows for to derive exact expressions for the Lieb-Robinson velocity and quantum speed limit, and figure of merit such as Krylov complexity. Our work reveals a strong dependence of the speed of information flow on the statistical distribution of resonance frequencies in the spin ensemble with immediate implications for the design of components for quantum technologies, realized for example with nitrogen vacancy centers, nuclear spins or ultracold atoms.