Quantum Leakage from Shamir Sharing with Correlated Resources
Abstract
We bound local quantum leakage from Shamir sharing uniformly over prime fields and permitted share-dependent channels. The adversary receives all outputs and a reference to a resource independent of the secret and sharing randomness. For independent device-reference pairs at fixed output dimension, we determine the exact exponent of the worst-case trace distance for two chosen secrets at every fixed reconstruction rate above one half, including its dependence on entanglement within each pair. For unentangled one-qubit leakage, this improves the sufficient rate of about $0.7334$ proved by Batra et al. Above one half, we also determine the exact exponent when an arbitrarily entangled support is tensored with single-device states elsewhere. Every fixed support fraction below the reconstruction rate gives exponential security, while a reconstruction set admits a known attack. Exponential security extends to fixed finite-memory processes with primitive transfer channels, fixed stationary chains satisfying upper operator mixing, and canonical primitive matrix product states, allowing arbitrary finite adversary extensions of the device marginal. For one-qubit outputs, fully separable resources and independent pairs whose joint output-reference states are positive under partial transpose for every share admit rates slightly below one half.
Related
- Quantum Leakage Resilience of Shamir Secret Sharing
- Improved Local Leakage Resilience of Shamir Secret Sharing and Worst-Case Optimal Polynomial Intersection
- Quantum secret sharing in a tripartite superconducting network
- Combinatorial aspects of holographic quantum secret sharing
- Collusion-Secure Semi-Quantum Secret Sharing Scheme using a Quantum Third Party
BibTeX
@misc{essayag2026quantum,
title = {{Quantum Leakage from Shamir Sharing with Correlated Resources}},
author = {Isaac Barouch Essayag and Aryeh Lev Zabokritskiy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06350},
eprint = {2610.06350},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06350},
}
RIS
TY - UNPB
TI - Quantum Leakage from Shamir Sharing with Correlated Resources
AU - Isaac Barouch Essayag
AU - Aryeh Lev Zabokritskiy
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06350
UR - https://arxiv.org/abs/2610.06350
AB - We bound local quantum leakage from Shamir sharing uniformly over prime fields and permitted share-dependent channels. The adversary receives all outputs and a reference to a resource independent of the secret and sharing randomness. For independent device-reference pairs at fixed output dimension, we determine the exact exponent of the worst-case trace distance for two chosen secrets at every fixed reconstruction rate above one half, including its dependence on entanglement within each pair. For unentangled one-qubit leakage, this improves the sufficient rate of about $0.7334$ proved by Batra et al. Above one half, we also determine the exact exponent when an arbitrarily entangled support is tensored with single-device states elsewhere. Every fixed support fraction below the reconstruction rate gives exponential security, while a reconstruction set admits a known attack. Exponential security extends to fixed finite-memory processes with primitive transfer channels, fixed stationary chains satisfying upper operator mixing, and canonical primitive matrix product states, allowing arbitrary finite adversary extensions of the device marginal. For one-qubit outputs, fully separable resources and independent pairs whose joint output-reference states are positive under partial transpose for every share admit rates slightly below one half.
ER -