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Computing on quantum shared secrets for general quantum access structures

Bassirian, R ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.1007/s11128-019-2224-7
  3. Publisher: Springer New York LLC , 2019
  4. Abstract:
  5. 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. © 2019, Springer Science+Business Media, LLC, part of Springer Nature
  6. Keywords:
  7. Access structures ; Error correction ; Quantum computation ; Seven qubit code ; Transversal computation ; Codes (symbols) ; Quantum computers ; Quantum optics ; Qubits ; Access structure ; Quantum secret sharing ; Quantum secret sharing schemes ; Quantum state ; Shared secrets ; Shared state ; Threshold schemes ; Quantum cryptography
  8. Source: Quantum Information Processing ; Volume 18, Issue 4 , 2019 ; 15700755 (ISSN)
  9. URL: https://link.springer.com/article/10.1007/s11128-019-2224-7