# Computing on quantum shared secrets

## TL;DR

This paper introduces a quantum secret-sharing scheme that enables computation on shared quantum secrets without decoding, ensuring security even with dishonest participants, advancing quantum cryptography protocols.

## Contribution

It proposes a novel (n,n)-quantum secret sharing scheme and protocols for performing quantum computations on shared secrets securely.

## Key findings

- Secure quantum computation on shared secrets demonstrated.
- Dishonest participants cannot learn the secret if at least one honest participant exists.
- Protocols maintain security against deviations from honest behavior.

## Abstract

A (k,n)-threshold secret-sharing scheme allows for a string to be split into n shares in such a way that any subset of at least k shares suffices to recover the secret string, but such that any subset of at most k-1 shares contains no information about the secret. Quantum secret-sharing schemes extend this idea to the sharing of quantum states. Here we propose a method of performing computation on quantum shared secrets. We introduce a (n,n)-quantum secret sharing scheme together with a set of protocols that allow quantum circuits to be evaluated on the shared secret without the need to decode the secret. We consider a multipartite setting, with each participant holding a share of the secret. We show that if there exists at least one honest participant, no group of dishonest participants can recover any information about the shared secret, independent of their deviations from the protocol.