dorsal/arxiv
View SchemaHow to share a quantum secret
| Authors | Richard Cleve, Daniel Gottesman, Hoi-Kwong Lo |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9901025 |
| URL | https://arxiv.org/abs/quant-ph/9901025 |
| DOI | 10.1103/PhysRevLett.83.648 |
| Journal | Phys.Rev.Lett. 83 (1999) 648-651 |
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, in all such cases, we give an efficient construction of a ((k,n)) threshold scheme. We also explore similarities and differences between quantum secret sharing schemes and quantum error-correcting codes. One remarkable difference is that, while most existing quantum codes encode pure states as pure states, quantum secret sharing schemes must use mixed states in some cases. For example, if k <= n < 2k-1 then any ((k,n)) threshold scheme must distribute information that is globally in a mixed state.
{
"annotation_id": "088eb94d-873e-4a17-9fad-860d4f168681",
"date_created": "2026-03-02T18:02:44.480000Z",
"date_modified": "2026-03-02T18:02:44.480000Z",
"file_hash": "4c88577ffe70eff8216a2858387763cc8b5b3dd4f07f5b76abed02f06eb821c0",
"private": false,
"record": {
"abstract": "We investigate the concept of quantum secret sharing. In a ((k,n)) threshold\nscheme, a secret quantum state is divided into n shares such that any k of\nthose shares can be used to reconstruct the secret, but any set of k-1 or fewer\nshares contains absolutely no information about the secret. We show that the\nonly constraint on the existence of threshold schemes comes from the quantum\n\"no-cloning theorem\", which requires that n \u003c 2k, and, in all such cases, we\ngive an efficient construction of a ((k,n)) threshold scheme. We also explore\nsimilarities and differences between quantum secret sharing schemes and quantum\nerror-correcting codes. One remarkable difference is that, while most existing\nquantum codes encode pure states as pure states, quantum secret sharing schemes\nmust use mixed states in some cases. For example, if k \u003c= n \u003c 2k-1 then any\n((k,n)) threshold scheme must distribute information that is globally in a\nmixed state.",
"arxiv_id": "quant-ph/9901025",
"authors": [
"Richard Cleve",
"Daniel Gottesman",
"Hoi-Kwong Lo"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevLett.83.648",
"journal_ref": "Phys.Rev.Lett. 83 (1999) 648-651",
"title": "How to share a quantum secret",
"url": "https://arxiv.org/abs/quant-ph/9901025"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "4eb712bf-1fd1-4bb2-a373-d959c5c35918",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}