Sparse and weak-measurement certification of graph-edge entanglement in PXP scar wavepackets
Abstract
An imperfect many-body revival does not by itself certify the entanglement of the returning state. We give a finite-record protocol for graph-edge localizable entanglement along scar wavepackets of a graph-dressed PXP chain. The target cluster state has nonzero energy variance, so neither an exact target eigenstate nor a dark-state embedding is assumed. Fresh binary probes of the undeformed Hamiltonians Pauli terms have a fully separable explanation, even within the dressed blockade sector. Adding local graph-stabilizer probes makes established entanglement witnesses accessible with simultaneous confidence bounds. For a specified square-root instrument, an imposed worst-case disturbance budget fixes the strength that minimizes the equal-allocation Hoeffding sufficient sampling cost. A local commutator bound accounts for finite-duration ancilla pulses while the Hamiltonian remains active. We test the protocol on chains through twenty spins, under perturbed dynamics, and with independent implementations. At the first twenty-spin return, synthetic weak records certify all nineteen graph edges. Generator, two-color, bounded-weight, and full-group benchmarks separate this localizable resource from genuine multipartite certification. The protocol measures recoverable entanglement in a known scar wavepacket, with explicit calibration and limits on its physical and statistical interpretation.
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BibTeX
@misc{wang2026sparse,
title = {{Sparse and weak-measurement certification of graph-edge entanglement in PXP scar wavepackets}},
author = {Ximo Wang and Yichi Zhang and Qiwei Han and Xi Zhao and Yuhang Wang and Chunxiao Du and Rui Li and Wenxiu Li and Hao Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24139},
eprint = {2609.24139},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24139},
}
RIS
TY - UNPB
TI - Sparse and weak-measurement certification of graph-edge entanglement in PXP scar wavepackets
AU - Ximo Wang
AU - Yichi Zhang
AU - Qiwei Han
AU - Xi Zhao
AU - Yuhang Wang
AU - Chunxiao Du
AU - Rui Li
AU - Wenxiu Li
AU - Hao Zhang
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24139
UR - https://arxiv.org/abs/2609.24139
AB - An imperfect many-body revival does not by itself certify the entanglement of the returning state. We give a finite-record protocol for graph-edge localizable entanglement along scar wavepackets of a graph-dressed PXP chain. The target cluster state has nonzero energy variance, so neither an exact target eigenstate nor a dark-state embedding is assumed. Fresh binary probes of the undeformed Hamiltonians Pauli terms have a fully separable explanation, even within the dressed blockade sector. Adding local graph-stabilizer probes makes established entanglement witnesses accessible with simultaneous confidence bounds. For a specified square-root instrument, an imposed worst-case disturbance budget fixes the strength that minimizes the equal-allocation Hoeffding sufficient sampling cost. A local commutator bound accounts for finite-duration ancilla pulses while the Hamiltonian remains active. We test the protocol on chains through twenty spins, under perturbed dynamics, and with independent implementations. At the first twenty-spin return, synthetic weak records certify all nineteen graph edges. Generator, two-color, bounded-weight, and full-group benchmarks separate this localizable resource from genuine multipartite certification. The protocol measures recoverable entanglement in a known scar wavepacket, with explicit calibration and limits on its physical and statistical interpretation.
ER -