Asymmetric Quantum Secure Multi-Party Computation With Weak Clients Against Dishonest Majority

27+10 pages, 5 figures. This work supersedes arXiv:2102.12949Secure 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