How to Share a Quantum Secret

Journal Article · Thu Jul 01 00:00:00 EDT 1999 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.83.648· OSTI ID:357603

Cleve, R ^[1]; Gottesman, D ^[2]; Lo, H ^[3]

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

We investigate the concept of quantum secret sharing. In a (k,thinspn) 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 k{minus}1 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 {open_quotes}no-cloning theorem,{close_quotes} which requires that n{lt}2k , and we give efficient constructions of all threshold schemes. We also show that, for k{le}n{lt}2k{minus}1 , then any (k,thinspn) threshold scheme {ital must} distribute information that is globally in a mixed state. {copyright} {ital 1999} {ital The American Physical Society }

• Research Organization: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 357603
• Journal Information: Physical Review Letters, Vol. 83, Issue 3; Other Information: PBD: Jul 1999
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
QUANTUM MECHANICS
SECRECY PROTECTION
INFORMATION THEORY
SECURITY
ERRORS