Computing on Quantum Shared Secrets for General Quantum Access Structures

TL;DR

This paper introduces new quantum secret sharing schemes for general access structures using 7-qubit CSS codes, enabling authorized subsets to perform universal quantum computation directly on shared secrets.

Contribution

It proposes a novel $(2,3)$ threshold scheme, extends it to $(n,n)$ schemes, and develops methods for authorized subsets to perform universal quantum computation without recovery.

Findings

Successfully constructed a $(2,3)$ quantum secret sharing scheme.

Extended to general quantum access structures via induction.

Enabled authorized subsets to perform universal quantum computation directly.

Abstract

Quantum secret sharing is a method for sharing a secret quantum state among a number of individuals such that certain authorized subsets of participants can recover the secret shared state by collaboration and other subsets cannot. In this paper, we first propose a method for sharing a quantum secret in a basic $(2,3)$ threshold scheme, only by using qubits and the 7-qubit CSS code. Based on this $(2,3)$ scheme, we propose a new $(n, n)$ scheme and we also construct a quantum secret sharing scheme for any quantum access structure by induction. Secondly, based on the techniques of performing quantum computation on 7-qubit CSS codes, we introduce a method that authorized subsets can perform universal quantum computation on this shared state, without the need for recovering it. This generalizes recent attempts for doing quantum computation on $(n, n)$ threshold schemes.