Research On Quantum Secret Sharing Schemes: Design And Information Theoretical Analysis

Quantum information science, which mainly consists of quantum communicationand quantum computing, has been developed quickly to be one of the newestcross-linked research fields in the past two decades. With the development of quantuminformation technology, the proposed concept of quantum secret sharing (QSS) providesa new idea and useful approach for managing keys securely. Currently, QSS has gainedthe attention from many scholars and obtained rich research results. However, most ofthe existing researches focus on ((n, n))quantum secret split schemes, but the studieson ((k, n))threshold QSS schemes and high dimension QSS schemes are quite few.This dissertation mainly investigates the threshold QSS schemes from theperspective of quantum information theory, including information theoretical model forschemes, quantum information rate, perfectly secure schemes. In addition,high-dimensional quantum secret sharing schemes are designed by using thefundamental laws of quantum mechanics. The highlights of the dissertation are asfollows:1. The information theoretical model for perfect QSS schemes based on coherentinformation is presented. In this model, ideal quantum information rate is obtained andthe ((k, n))threshold QSS schemes based on quantum MDS codes is proven to beunconditional secure.2. Mathematical characterization of perfect QSS schemes is given by utilizingquantum information quantity inequality, Araki-Lieb inequality. Based on thischaracterization, we present a proof that a ((t+1,2t+1))threshold QSS scheme existsif and only if a [[2t+1,1, t+1]]quantum MDS code exists, where t is a positiveinteger.3. Based on the model of perfect QSS schemes, non-perfect ((k, L, n))thresholdramp QSS schemes are defined, where (n+L)/2≤k≤n. We also obtain the idealquantum information rate of ((k, L, n))threshold ramp QSS schemes, and construct aquantum ramp QSS scheme using quantum MDS codes.4. In view of the fact of the similarity between the wire-tap channel of type IIconcept and ramp secret sharing schemes, and inspired by the application of coset coding to the wire-tap channel of type II, a ramp QSS scheme based on the nestedencoding structure and decoding threshold property of quantum LDPC codes isproposed.5. A multiparty QSS scheme of sharing classical messages based on ddimensional multi-particle entanglement states is proposed. The theoretical efficiency ofthe present scheme achieves almost100%. Analysis results show that the presentedscheme is secure against intercept-resend attacks and entanglement attack. Moreover,we discuss the possibility of successful sharing of classical messages where the QSSscheme is carried out in generalized Pauli channels. It shows that channel noise has noeffect on the implement of the present scheme if the channel is bit-phase channel.6. With the help of quantum teleportation thought, we successfully develop amultiparty QSS scheme of sharing a maximal entangled state based on d dimensionalmulti-particle entangled states. This scheme can be implemented by using only localoperations and classical communication (LOCC) between participants. Analysis resultsshow that this scheme is a non-perfect QSS scheme.