Quantum Secure Non-Interactive Reductions

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.