1202.3433 (Pradeep Sarvepalli)

Non-Threshold Quantum Secret Sharing Schemes in the Graph State
Formalism    [PDF]

Pradeep Sarvepalli

In a recent work, Markham and Sanders have proposed a framework to study
quantum secret sharing (QSS) schemes using graph states. This framework unified
three classes of QSS protocols, namely, sharing classical secrets over private
and public channels, and sharing quantum secrets. However, most work on secret
sharing based on graph states focused on threshold schemes. In this paper, we
focus on general access structures. We show how to realize a large class of
arbitrary access structures using the graph state formalism. We show an
equivalence between $[[n,1]]$ binary quantum codes and graph state secret
sharing schemes sharing one bit. We also establish a similar (but restricted)
equivalence between a class of $[[n,1]]$ Calderbank-Shor-Steane (CSS) codes and
graph state QSS schemes sharing one qubit. With these results we are able to
construct a large class of quantum secret sharing schemes with arbitrary access
structures.

View original: http://arxiv.org/abs/1202.3433