[10]Connectivity Engineering: Inverse Reconstruction of Discrete Bulk Topology from Entanglement Fingerprints

Wenjun Luo

Published Oct 25, 2026• 0 citations

Abstract

In the framework of connectivity engineering, this paper proposes a method to inversely reconstruct the internal discrete topological connectivity from the boundary entanglement entropy spectrum. Based on a one-dimensional spin-1/2 network, we extract a three-dimensional entanglement fingerprint characterizing the internal connectivity: the mutual information peak, the peak position, and the late-time residual fidelity. Numerical diagnostics show that when the connectivity reaches k=3, the mutual information peak reaches 1.49 times that of the baseline network, and the system enters the topological saturation regime; at this point, the fingerprint vectors for k=3 and k=4 are indistinguishable within numerical precision. We prove that this degeneracy originates from the joint mechanism of graph-theoretic topology and dynamical decay, and further increasing k does not yield substantial cross-region entanglement channels. Even in the presence of numerical noise, the significant gap in late-time fidelity between k=2 and the saturation regime ensures the high robustness of the inverse mapping. This result establishes the effectiveness of the "entanglement fingerprint distance" as an inverse diagnostic operator, providing an operational benchmark for discrete bulk geometry reconstruction using purely boundary observables.

DOI: 10.5281/zenodo.23643056

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