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 always 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. 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.

Tags: Building Blocks, Multi Party, Quantum Enhanced Classical Functionality

Use Cases

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

Protocols

(under construction)

Properties

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 $n$ parties and any team of $t$ parties or more, with $t\leq n$, has full access to the secret, whereas $t-1$ collaborating parties or less have no information about the secret at all. Such $(t,n)$-threshold schemes are not possible 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 at the same. So in contrast to CSS, there are always $n$ parties in QSS that all must collaborate by adhering to the protocol, in order that one party will receive the secret from Alice.

References

1. Mayers (2001)
2. Joy et al (2018)
3. Gottesman (1999)
4. Hillery et al (1998)

contributed by Peter Limacher