Paper 2023/1490

Formulations and Constructions of Remote State Preparation with Verifiability, with Applications

Abstract

Remote state preparation with verifiability (RSPV) is an important quantum cryptographic primitive [GV19,Zha22]. In this primitive, a client would like to prepare a quantum state (sampled or chosen from a state family) on the server side, such that ideally the client knows its full description, while the server holds and only holds the state itself. In this work we make several contributions on its formulations, constructions and applications. In more detail: - We first work on the definitions and abstract properties of the RSPV problem. We select and compare different variants of definitions [GV19,GMP22,Zha22], and study their basic properties (like composability and amplification). - We also study a closely related question of how to certify the server's operations (instead of solely the states). We introduce a new notion named remote operator application with verifiability (ROAV). We compare this notion with related existing definitions [SW87,MY04,MV21,NZ23], study its abstract properties and leave its concrete constructions for further works. - Building on the abstract properties and existing results [BGKPV23], we construct a series of new RSPV protocols. Our constructions not only simplify existing results [GV19] but also cover new state families, for example, states in the form of $\frac{1}{\sqrt{2}}(|0\rangle|x_0\rangle+|1\rangle|x_1\rangle)$. All these constructions rely only on the existence of weak NTCF [BKVV,AMR22], without additional requirements like the adaptive hardcore bit property [BCMVV,AMR22]. - As a further application, we show that the classical verification of quantum computations (CVQC) problem [ABEM,Mah18] could be constructed from assumptions on group actions [ADMP20]. This is achieved by combining our results on RSPV with group-action-based instantiation of weak NTCF [AMR22], and then with the quantum-gadget-assisted quantum verification protocol [FKD18].