Secure multi-party computation (SMPC) protocols allow several parties that distrust each other to collectively compute a function on their inputs. In this paper, we introduce a protocol that lifts classical SMPC to quantum SMPC in a composably and statistically secure way, even for a single honest party. Unlike previous quantum SMPC protocols, our proposal only requires very limited quantum resources from all but one party; it suffices that the weak parties, i.e. the clients, are able to prepare single-qubit states in the X-Y plane. The novel quantum SMPC protocol is constructed in a naturally modular way, and relies on a new technique for quantum verification that is of independent interest. This verification technique requires the remote preparation of states only in a single plane of the Bloch sphere. In the course of proving the security of the new verification protocol, we also uncover a fundamental invariance that is inherent to measurement-based quantum computing.

翻译：安全多方计算协议允许互不信任的多个参与方共同计算其输入上的函数。本文提出了一种将经典安全多方计算提升至量子安全多方计算的协议，该协议在组合安全性和统计安全性方面均具有保障，即便仅存在单个诚实参与方也能成立。与先前的量子安全多方计算协议不同，我们的方案仅要求除一方外的所有参与方具备极有限的量子资源；弱参与方（即客户端）只需能够制备X-Y平面上的单量子比特态即可。这一新型量子安全多方计算协议采用自然模块化的方式构建，并依赖于一种具有独立研究价值的量子验证新技术。该验证技术仅需在布洛赫球的一个平面上远程制备量子态。在证明该新验证协议安全性的过程中，我们还揭示了一个内禀于基于测量的量子计算的基本不变性。