# HOW TO SHARE A QUANTUM SECRET

@article{Cleve1999HOWTS, title={HOW TO SHARE A QUANTUM SECRET}, author={Richard Cleve and Daniel Gottesman and Hoi-Kwong Lo}, journal={Physical Review Letters}, year={1999}, volume={83}, pages={648-651} }

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…

## 1,002 Citations

Quantum strongly secure ramp secret sharing

- Computer ScienceQuantum Inf. Process.
- 2015

This paper introduces a quantum analog of classical strong security in ramp secret sharing schemes, and ensures that qudits with critical information can no longer be leaked.

Verifiable quantum (k, n)-threshold secret sharing

- Computer ScienceQuantum Inf. Process.
- 2012

This paper shows how to construct a verifiable quantum (k, n) threshold scheme by combining a qubit authentication process and can provide a mechanism for checking whether the reconstructed quantum secret is same with the original one.

New Protocols and Lower Bounds for Quantum Secret Sharing with Graph States

- Computer Science, MathematicsTQC
- 2012

A new family of quantum secret sharing protocols with limited quantum resources which extends the protocols proposed by Markham and Sanders [14] and Broadbent, Chouha, and Tapp and proves that for any threshold k ≥ n − n 0.68 there exists a graph allowing a ((k,n)) protocol.

Quantum secret sharing based on local distinguishability

- MathematicsArXiv
- 2014

This paper analyzes the (im)possibility of the exact distinguishability of orthogonal multipartite entangled states under {\em restricted local operation and classical communication} and proposes a new scheme for quantum secret sharing (QSS).

Universal Communication Efficient Quantum Threshold Secret Sharing Schemes

- Computer Science, Mathematics2020 IEEE Information Theory Workshop (ITW)
- 2021

This paper proposes a more general class of ((k, n) quantum secret sharing schemes with low communication complexity, where the combiner can contact any d parties at the time of recovery where k ≤ d ≤ n.

Rational Quantum Secret Sharing

- Computer Science, Mathematics
- 2019

Quantum Secret Sharing attempts to extend a (k, n)-threshold scheme as an encoding scheme under which a secret S is converted into n shares, with which the original message S can only be recovered if k parties collaborate.

Theory of quantum secret sharing

- Computer Science
- 2000

It is shown that any mixed state quantum secret sharing scheme can be derived by discarding a share from a pure state scheme, and that the size of each share in a quantumSecretSharing scheme must be at least as large as thesize of the secret.

Communication Efficient Quantum Secret Sharing

- Computer SciencePhysical Review A
- 2019

The proposed schemes are communication efficient with respect to standard schemes; and when d=2k\ensuremath{-}1$, the quantum communication cost is reduced by a factor $O(k)$.

Weighted Threshold Quantum Secret Sharing Based on the Chinese Remainder Theorem and the Phase Shift Operation

- Computer Science2018 IEEE International Conference on Systems, Man, and Cybernetics (SMC)
- 2018

This study uses the Chinese Remainder Theorem and performs the phase shift operation on a quantum state to build a weighted threshold secret sharing scheme that is an efficient and flexible weighted threshold quantum secret sharing and is simpler and easier to implement than earlier ones.

Efficient Quantum Secret Sharing

- Computer Science
- 2018

In the proposed schemes, the secret is recovered by communicating d d−k+1 qudits for every qudit of the secret, where d ≥ k, and it is shown that these schemes are optimal.

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