Quantum Secure Non-Interactive Reductions
Abstract
Efficient models for secure computation often rely on offline preprocessed correlations, which subsequently enable private online computation from minimal assumptions. Within these models, the study of secure non-interactive reductions (SNIR) formalizes when one classical correlation can be non-interactively transformed into another, while guaranteeing information-theoretic simulation-based privacy. In this work, we introduce quantum secure non-interactive reductions (QSNIR), a natural extension of SNIR, in which the source and target resource are each a bipartite quantum state. Specifically, when the target resource is classical, our framework enables us to analyze the problem of disseminating private correlations from entanglement, in addition to classical resources. Our primary technical result is that QSNIR privacy in this context can be computed exactly via a semidefinite program (SDP) pair that quantifies an error operationally rooted in a simulation-based cheating advantage. We prove that QSNIR privacy is lower-bounded by a decision problem related to minimum-error state discrimination (MED), and use both definitions to compute exact one-shot privacy errors for universal two-party computation (2PC) preprocessing correlations.
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BibTeX
@misc{gold2026quantum,
title = {{Quantum Secure Non-Interactive Reductions}},
author = {Maxwell Gold and Sarah Hagen and Daniel Alabi and Eric Chitambar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38452},
eprint = {2609.38452},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38452},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Secure Non-Interactive Reductions
AU - Maxwell Gold
AU - Sarah Hagen
AU - Daniel Alabi
AU - Eric Chitambar
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38452
UR - https://arxiv.org/abs/2609.38452
AB - Efficient models for secure computation often rely on offline preprocessed correlations, which subsequently enable private online computation from minimal assumptions. Within these models, the study of secure non-interactive reductions (SNIR) formalizes when one classical correlation can be non-interactively transformed into another, while guaranteeing information-theoretic simulation-based privacy. In this work, we introduce quantum secure non-interactive reductions (QSNIR), a natural extension of SNIR, in which the source and target resource are each a bipartite quantum state. Specifically, when the target resource is classical, our framework enables us to analyze the problem of disseminating private correlations from entanglement, in addition to classical resources. Our primary technical result is that QSNIR privacy in this context can be computed exactly via a semidefinite program (SDP) pair that quantifies an error operationally rooted in a simulation-based cheating advantage. We prove that QSNIR privacy is lower-bounded by a decision problem related to minimum-error state discrimination (MED), and use both definitions to compute exact one-shot privacy errors for universal two-party computation (2PC) preprocessing correlations.
ER -