Combinatorial aspects of holographic quantum secret sharing
Abstract
We introduce combinatorial holographic quantum secret sharing (CHQSS) for a bulk subregion in AdS3/CFT2 to study how logical information of the bulk subregion is encoded in the boundary and protected from erasures of boundary subregions. We introduce a distance, a reconstruction threshold, and a secret threshold to characterize CHQSS schemes. We present the phase transitions of multipartite entanglement wedges in a symmetric setup and observe multiple distinct phase transition points. The distance and thresholds depend on the holographic phase and the choice of bulk subregion. We derive the maximum distance. Moreover, we derive the relations between the distance and the thresholds. We construct a family of CHQSS schemes in the symmetric setting that includes perfect threshold CHQSS and perfect non-threshold CHQSS.
Related
- Quantum secret sharing in a tripartite superconducting network
- Traceable Quantum Secret Sharing
- Quantum Secret Sharing with a Helper and Programmable Access Structures
- Collusion-Secure Semi-Quantum Secret Sharing Scheme using a Quantum Third Party
- A Three-Party W-State Quantum Secret Sharing Protocol with X-Gate Encoding and Forbidden-Outcome Detection
BibTeX
@misc{bao2026combinatorial,
title = {{Combinatorial aspects of holographic quantum secret sharing}},
author = {Ning Bao and Keiichiro Furuya and Jacob March},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.16110},
eprint = {2607.16110},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.16110},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Combinatorial aspects of holographic quantum secret sharing
AU - Ning Bao
AU - Keiichiro Furuya
AU - Jacob March
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2607.16110
UR - https://arxiv.org/abs/2607.16110
AB - We introduce combinatorial holographic quantum secret sharing (CHQSS) for a bulk subregion in AdS_3/CFT_2 to study how logical information of the bulk subregion is encoded in the boundary and protected from erasures of boundary subregions. We introduce a distance, a reconstruction threshold, and a secret threshold to characterize CHQSS schemes. We present the phase transitions of multipartite entanglement wedges in a symmetric setup and observe multiple distinct phase transition points. The distance and thresholds depend on the holographic phase and the choice of bulk subregion. We derive the maximum distance. Moreover, we derive the relations between the distance and the thresholds. We construct a family of CHQSS schemes in the symmetric setting that includes perfect threshold CHQSS and perfect non-threshold CHQSS.
ER -