Information-theoretically-sound non-interactive classical verification of quantum computing with trusted center

The posthoc verification protocol [J. F. Fitzsimons, M. Hajdu{\v s}ek, and T. Morimae, Physical Review Letters {\bf120}, 040501 (2018)] enables an information-theoretically-sound non-interactive verification of quantum computing, but the message from the prover to the verifier is quantum and the verifier has to do single-qubit measurements. The Mahadev protocol removes these quantum parts, but the soundness becomes the computational one. In this paper, we construct an information-theoretically-sound non-interactive classical verification protocol for quantum computing with a trusted center. The trusted center sends random BB84 states to the prover, and the classical descriptions of these BB84 states to the verifier. The messages from the center to the prover and the verifier are independent of the instance. By slightly modifying our protocol, we also construct a non-interactive statistical zero-knowledge proof system for QMA with the trusted center.