# QFactory: classically-instructed remote secret qubits preparation

## TL;DR

This paper introduces a secure protocol for classically instructing a quantum server to prepare random secret qubits, based on trapdoor functions and the Learning With Errors problem, with extensions for larger state sets and verifiability.

## Contribution

It presents a simplified primitive using BB84 states, a secure protocol against malicious servers, and new extensions including verifiability and larger state sets.

## Key findings

- Protocol is secure against arbitrary malicious servers.
- Security is based on the hardness of Learning With Errors.
- Introduces blind self-testing for verifiability.

## Abstract

The functionality of classically-instructed remotely prepared random secret qubits was introduced in (Cojocaru et al 2018) as a way to enable classical parties to participate in secure quantum computation and communications protocols. The idea is that a classical party (client) instructs a quantum party (server) to generate a qubit to the server's side that is random, unknown to the server but known to the client. Such task is only possible under computational assumptions. In this contribution we define a simpler (basic) primitive consisting of only BB84 states, and give a protocol that realizes this primitive and that is secure against the strongest possible adversary (an arbitrarily deviating malicious server). The specific functions used, were constructed based on known trapdoor one-way functions, resulting to the security of our basic primitive being reduced to the hardness of the Learning With Errors problem. We then give a number of extensions, building on this basic module: extension to larger set of states (that includes non-Clifford states); proper consideration of the abort case; and verifiablity on the module level. The latter is based on "blind self-testing", a notion we introduced, proved in a limited setting and conjectured its validity for the most general case.

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Source: https://tomesphere.com/paper/1904.06303