From Local Nonclassicality to Entanglement: A Convexity Law for Single-Excitation Dynamics

TL;DR

This paper establishes a convexity law linking local nonclassicality and entanglement in excitation-preserving quantum dynamics, providing analytical and numerical insights into resource redistribution and practical diagnostics.

Contribution

It introduces a convexity bound for local negativities in single-excitation dynamics, connecting nonclassicality to entanglement growth and offering a new diagnostic tool.

Findings

The sum of local negativities is bounded by the initial excitation negativity.

Entanglement growth corresponds to redistribution of a fixed resource.

Deviations from the bound indicate decoherence or control errors.

Abstract

We prove a simple dynamical law for excitation-preserving interactions: the {sum of local Wigner negativities} is upper-bounded by a fixed budget set by the initially excited state. For the single-excitation sector of the XY model (and its beam-splitter analogue), this convexity bound equals the negativity of the seed state and is saturated only when the excitation is fully localized. At intermediate times the sum lies strictly below the bound due to phase-space overlap in local mixtures, quantitatively accounting for entanglement growth as a redistribution of a finite, budgeted resource into shared correlations. We establish the result analytically for two bodies and corroborate it numerically in engineered state-transfer chains, where it reveals a coherence-enabled dark transport: the resource becomes locally invisible while being stored in multi-body coherences. The predicted trajectory of the summed local negativity provides a practical hardware metric: deviations from the ideal, budgeted curve diagnose decoherence and control error.