# Techniques: Asymmetric Quantum Secure Multi-Party Computation With Weak Clients Against Dishonest Majority

## What the paper contributes (one paragraph)
The paper (arXiv:2303.08865) gives a protocol that lifts a classical secure multi-party computation (SMPC) protocol to a quantum SMPC protocol for BQP computations in a composably and statistically secure way. It targets the asymmetric clients-server setting: all clients except one powerful server are weakly quantum and need only prepare single-qubit states in the X-Y plane of the Bloch sphere. Security holds whenever a single client is trustworthy, so it withstands collusion between corrupt clients and the server, providing both blindness and verification, and tolerating a fixed amount of global noise. Two ingredients of independent interest are introduced: a Collaborative Remote State Preparation gadget that securely implements remote preparation of single-qubit states, and the first dummyless secure delegated quantum computation (SDQC) verification protocol, which relies on a newly uncovered invariance of measurement-based quantum computing. Everything is proved in the Abstract Cryptography framework.

## Techniques offered
- **Secure multi-party computation (quantum SMPC lift)** - composably and statistically secure protocol that turns a classical SMPC into a quantum SMPC for BQP computations in the weak-client, dishonest-majority setting.
  - guarantee: composable statistical (information-theoretic) security in the Abstract Cryptography framework, providing blindness and verification as long as a single client is trustworthy, robust to a fixed amount of global noise.
  - quote: "In this paper, we introduce a protocol that lifts classical SMPC to quantum SMPC in a composably and statistically secure way, even for a single honest party." <!-- style-ban: allow verbatim quote from source -->
- **Dummyless secure delegated quantum computation (single-plane SDQC verification)** - a verifiable blind delegated computation protocol in which the client prepares only X-Y plane states, removing the need for computational-basis dummy qubits as traps.
  - guarantee: statistical (composable) soundness in the Abstract Cryptography framework via test rounds that perform stabiliser measurements, exploiting a proved invariance of MBQC to the one uncatchable Z-type deviation for classical input/output computations.
  - quote: "The second new ingredient of our proof is the first dummyless SDQC protocol."
- **Collaborative Remote State Preparation (CRSP)** - a multi-client networking gadget that lets a classical party request an arbitrary single-qubit state to be prepared on the server's device with help from clients preparing X-Y plane states.
  - guarantee: statistically secure implementation of the Remote State Preparation resource in the Abstract Cryptography framework, providing privacy amplification of the classical-quantum correlations clients share with the server.
  - quote: "In \\S~\\ref{subsec:coll-st-prep}, we introduce a Collaborative Remote State Preparation (CRSP) protocol."

## Where it could apply
- Target primitive(s): any BQP computation expressed in the measurement-based (MBQC) model; verifiable blind delegated execution of such computations
- Target application group(s): platforms_tooling, quantum_cryptography / quantum_networking, distributed_quantum_computing
- Code family / hardware assumptions: no error-correcting code required (noise-robust on near-term devices); clients need only single-qubit X-Y plane state preparation; assumes a powerful quantum server, suited to photonic or other platforms where single-axis rotations are easier

## Caveats
The protocol verifies BQP computations with classical inputs and outputs; the dummyless verification relies on the proved MBQC invariance that holds for classical input/output computations, and the authors give evidence that an analogous CRSP gadget for quantum inputs and outputs (correlations outside a single Bloch-sphere plane) may be hard or impossible to construct. Security comes at the cost of a polynomial number of repetitions, and the noise tolerance is fixed rather than scalable, so it supports experimental proof-of-concepts rather than large fault-tolerant computations.