How to Share a Quantum Secret
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 k-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 ``no-cloning theorem,'' which requires that n<2k, and we give efficient constructions of all threshold schemes. We also show that, for k<=n<2k-1, then any \(k,n\) threshold scheme must distribute information that is globally in a mixed state.
- Publication:
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Physical Review Letters
- Pub Date:
- July 1999
- DOI:
- 10.1103/PhysRevLett.83.648
- arXiv:
- arXiv:quant-ph/9901025
- Bibcode:
- 1999PhRvL..83..648C
- Keywords:
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- Quantum Physics
- E-Print:
- 5 pages, REVTeX, submitted to PRL