Editing Quantum Secret Sharing

==Functionality Description==
Quantum Secret Sharing (QSS) allows to transfer a quantum state (or a classical message encoded as quantum state), referred to as the secret, from Alice to Bob but only with the consent of a third-party, Charlie. A QSS protocol is generalizable to an arbitrary number of parties consisting of one sender, one recipient, and all other parties being endorsers. In case of only two parties, sender and receiver, QSS is equivalent to [[Quantum Teleportation]]. Despite the no-cloning theorem not allowing the quantum secret to be in possession of more than one party at the same time, there exist QSS protocols that mimic classical secret sharing (see [[Quantum Secret Sharing#Further Details|Further Information]]).

'''Tags:'''  [[:Category: Building Blocks|Building Blocks]], [[:Category: Multi Party Protocols|Multi Party]], [[:Category: Quantum Enhanced Classical Functionality|Quantum Enhanced Classical Functionality]]

[[Category: Two Party Protocols]] [[Category: Quantum Enhanced Classical Functionality]]

== Use Cases ==
* QSS can replace certain classical secret sharing scenarios with unconditional security.[[Quantum Secret Sharing#References|(1)]]
* Secret sharing is a very common building block in other protocols:[[Quantum Secret Sharing#References|(2)]]
** [[Secure Multiparty Delegated Quantum Computation]]
** Leader election and [[Fast Quantum Byzantine Agreement|Byzantine Agreement]]
** Error correction in quantum computers[[Quantum Secret Sharing#References|(3)]]
** Bank transfers with third party endorsement, see [[Quantum Cheque]]

==Protocols==
#[[Quantum Secret Sharing using GHZ States]][[Quantum Secret Sharing#References|(4)]]
#[[Verifiable Quantum Secret Sharing]] (VQSS)

==Properties==
* Confidentiality: QSS with one dishonest party not following the protocol must guarantee that no information about the quantum secret at all is revealed to any party. 
* Security: Every protocol must ensure that no information about the secret is leaked to an external eavesdropper.

==Further Information==
QSS is inspired by classical secret sharing (CSS), but has one fundamental difference due to the no-cloning theorem. In CSS, Alice shares a secret among <math>n</math> parties and any team of <math>t</math> parties or more, with <math>t \leq n</math>, has full access to the secret, whereas <math>t-1</math> collaborating parties or less have no information about the secret at all. Such <math>(t, n)</math>-threshold schemes are not straightforward to implement for QSS, since the no-cloning theorem forbids that quantum states are copied, resulting in only one party, the receiver, obtaining the quantum secret from Alice, who looses hers during the process. However, <math>(t, n)</math> schemes can be built through sequentially running several QSS rounds.[[Quantum Secret Sharing#References|(5)]]

==References==
#[https://arxiv.org/abs/quant-ph/9802025 Mayers (2001)]
#[https://arxiv.org/abs/1807.03219 Joy et al (2018)]
#[https://arxiv.org/abs/quant-ph/9910067 Gottesman (1999)]
#[https://arxiv.org/abs/quant-ph/9806063 Hillery et al (1998)]
#[https://arxiv.org/abs/1710.11600 Lu et al (2018)]

<div style='text-align: right;'>''contributed by Peter Limacher''</div>