How to Share a Quantum Secret

Richard Cleve, Daniel Gottesman, and Hoi-Kwong Lo
Phys. Rev. Lett. 83, 648 – Published 19 July 1999
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Abstract

We investigate the concept of quantum secret sharing. In a (k,n) threshold scheme, a secret quantum state is divided into n shares such that any k of those shares can be used to reconstruct the secret, but any set of k1 or fewer shares contains absolutely no information about the secret. We show that the only constraint on the existence of threshold schemes comes from the quantum “no-cloning theorem,” which requires that n<2k, and we give efficient constructions of all threshold schemes. We also show that, for kn<2k1, then any (k,n) threshold scheme must distribute information that is globally in a mixed state.

  • Received 11 January 1999

DOI:https://doi.org/10.1103/PhysRevLett.83.648

©1999 American Physical Society

Authors & Affiliations

Richard Cleve1,*, Daniel Gottesman2,†, and Hoi-Kwong Lo3,‡

  • 1Department of Computer Science, University of Calgary, Calgary, Alberta, Canada T2N 1N4
  • 2T-6 Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
  • 3Hewlett-Packard Labs, Bristol BS34 8QZ, United Kingdom

  • *Email address: cleve@cpsc.ucalgary.ca
  • Email address: gottesma@t6-serv.lanl.gov
  • Email address: hkl@hplb.hpl.hp.com

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Vol. 83, Iss. 3 — 19 July 1999

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Heating up of Superconductors
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This collection marks the 30th anniversary of the discovery of high-temperature superconductors. The papers selected highlight some of the advances that have been made to date, both in understanding why these compounds behave in the way they do, and in utilizing them in applications. The papers included in the collection have been made free to read.

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