Computationally-secure and composable remote state preparation

Understand

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.