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

• URL: http://arxiv.org/abs/2511.10470v1
• Date: Fri, 14 Nov 2025 01:53:13 GMT
• Title: From Local Nonclassicality to Entanglement: A Convexity Law for Single-Excitation Dynamics
• Authors: Atta ur Rahman, Ao-xiang Liu, M. Y. Abd-Rabbou, Cong-feng Qiao,
• Abstract summary: We prove a simple dynamical law for excitation-preserving interactions.<n>The sum of local Wigner negativities is upper-bounded by a fixed budget set by the initially excited state.<n>The predicted trajectory of the summed local negativity provides a practical hardware metric.
• Score: 0.5541461456285174
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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