# Computationally-secure and composable remote state preparation. (arXiv:1904.06320v1 [quant-ph])

We introduce a protocol between a classical polynomial-time verifier and a

quantum polynomial-time prover that allows the verifier to securely delegate to

the prover the preparation of certain single-qubit quantum states. The protocol

realizes the following functionality, with computational security: the verifier

chooses one of the observables $Z$, $X$, $Y$, $(X+Y)/\sqrt{2}$,

$(X-Y)/\sqrt{2}$; the prover receives a uniformly random eigenstate of the

observable chosen by the verifier; the verifier receives a classical

description of that state. The prover is unaware of which state he received and

moreover, the verifier can check with high confidence whether the preparation

was successful. The delegated preparation of single-qubit states is an

elementary building block in many quantum cryptographic protocols. We expect

our implementation of "random remote state preparation with verification", a

functionality first defined in (Dunjko and Kashefi 2014), to be useful for

removing the need for quantum communication in such protocols while keeping

functionality. The main application that we detail is to a protocol for blind

and verifiable delegated quantum computation (DQC) that builds on the work of

(Fitzsimons and Kashefi 2018), who provided such a protocol with quantum

communication. Recently, both blind an verifiable DQC were shown to be

possible, under computational assumptions, with a classical polynomial-time

client (Mahadev 2017, Mahadev 2018). Compared to the work of Mahadev, our

protocol is more modular, applies to the measurement-based model of computation

(instead of the Hamiltonian model) and is composable. Our proof of security

builds on ideas introduced in (Brakerski et al. 2018).