Graph State-Based Quantum Secret Sharing with the Chinese Remainder Theorem

Quantum secret sharing (QSS) is a significant quantum cryptography technology in the literature. Dividing an initial secret into several sub-secrets which are then transferred to other legal participants so that it can be securely recovered in a collaboration fashion. In this paper, we develop a quantum route selection based on the encoded quantum graph state, thus enabling the practical QSS scheme in the small-scale complex quantum network. Legal participants are conveniently designated with the quantum route selection using the entanglement of the encoded graph states. Each participant holds a vertex of the graph state so that legal participants are selected through performing operations on specific vertices. The Chinese remainder theorem (CRT) strengthens the security of the recovering process of the initial secret among the legal participants. The security is ensured by the entanglement of the encoded graph states that are cooperatively prepared and shared by legal users beforehand with the sub-secrets embedded in the CRT over finite fields.     

Quantum Secret Sharing Based on Chinese Remainder Theorem

A novel quantum secret sharing (QSS) scheme is proposed on the basis of Chinese Remainder Theorem (CRT). In the scheme, the classical messages are mapped to secret sequences according to CRT equations, and distributed to different receivers by different dimensional superdense-coding respectively. CRT's secret sharing function,together with high-dimensional superdense-coding, provide convenience, security, and large capability quantum channel forsecret distribution and recovering. Analysis shows the security of the scheme.     

Experimental quantum secret sharing and third-man quantum cryptography

Quantum secret sharing (QSS) and third-man quantum cryptography (TQC) are essential for advanced quantum communication; however, the low intensity and fragility of the multiphoton entanglement source in previous experiments have made their realization an extreme experimental challenge. Here, we develop and exploit an ultrastable high intensity source of four-photon entanglement to report an experimental realization of QSS and TQC. The technology developed in our experiment will be important for future multiparty quantum communication.     

The Dining Cryptographer Problem-Based Anonymous Quantum Communication via Non-maximally Entanglement State Analysis

We demonstrate an anonymous quantum communication (AQC) via the non-maximally entanglement state analysis (NESA) based on the dining cryptographer problem (DCP). The security of the present AQC is ensured due to the quantum-mechanical impossibility of local unitary transformations between non-maximally entanglement states, which provides random numbers for the secure AQC. The analysis shows that the DCP-based AQC can be performed without intractability through the NESA in the multi-photon entangled quantum system.     

Quantum Discord and Entanglement of Quasi-Werner States Based on Bipartite Entangled Coherent States

Present work is an attempt to compare quantum discord and quantum entanglement of quasi-Werner states formed with the four bipartite entangled coherent states (ECS) used recently for quantum teleportation of a qubit encoded in superposed coherent state. Out of these, the quasi-Werner states based on maximally ECS due to its invariant nature under local operation is independent of measurement basis and mean photon numbers, while for quasi-Werner states based on non-maximally ECS, it depends upon measurement basis as well as on mean photon number. However, for large mean photon numbers since non-maximally ECS becomes almost maximally entangled therefore dependence of quantum discord for non-maximally ECS based quasi-Werner states on the measurement basis disappears.     

Scheme for realizing entanglement concentration via generalized measurements

How to concentrate non-maximally entangled states for quantum communication is a fundamental problem in quantum information. In this paper, we will apply generalized measurements to entanglement concentration of known non-maximally entangled pure states in arbitrary dimensional system. How to design the generalized measurements for the unambiguous discrimination of linearly independent non-orthogonal states is crucial for the concentration of the known non-maximally entangled states. The result shows that, any known non-maximally entangled pure state (for arbitrary dimensional system) can be transformed to the maximally entangled state only by introducing a qubit as ancilla and a joint unitary transformation operation on one of the entangled particles and the ancilla. In addition, because the less entangled state of each fail round will be re-concentrated too, the entanglement waste during the concentration process will be greatly reduced.     

基于量子图态的量子秘密共享

本文基于量子图态的几何结构特征,利用生成矩阵分割法,提出了一种量子秘密共享方案.利用量子图态基本物理性质中的稳定子实现信息转移的模式、秘密信息的可扩展性以及新型的组恢复协议,为安全的秘密共享协议提供了多重保障.更重要的是,方案针对生成矩阵的循环周期问题和因某些元素不存在本原元而不能构造生成矩阵的问题提出了有效的解决方案.在该方案中,利用经典信息与量子信息的对应关系提取经典信息,分发者根据矩阵分割理论获得子秘密集,然后将子秘密通过酉操作编码到量子图态中,并分发给参与者,最后依据该文提出的组恢复协议及图态相关理论得到秘密信息.理论分析表明,该方案具有较好的安全性及信息的可扩展性,适用于量子网络通信中的秘密共享,保护秘密数据并防止泄露.     

Quantum Secret Sharing Based on Quantum Search Algorithm

Quantum secret sharing (QSS) and quantum search algorithm (QSA) are considered as two important but different research topics in quantum information science. This paper recognizes an important feature in the well-known Grover’s QSA and then applies it to propose a QSS protocol. In contrast to the existing QSA-based QSS protocols, the newly proposed protocol has the following two advantages: (1)?no quantum memory is required by the agents, whereas the agents in the existing QSA-based QSS protocols need long-term quantum memories to store their secret shadows; (2)?the agents can cooperate to recover the boss’s secret by using shadows in classical bits, whereas, the others have to combine their shadows in photons and perform a unitary operation on the retained photons. The proposed QSS protocol is also shown to be secure against eavesdroppers or malicious agents.     

A （2, 3） quantum threshold scheme based on Greenberger-Horne-Zeilinger state

In this paper, by using properties of quantum controlled-not manipulation and entanglement states, we have designed a novel (2, 3) quantum threshold scheme based on the Greenberger- Horne -Zeilinger (GHZ) state. The proposed scheme involves two phases, i.e. a secret sharing phase and a secret phase. Detailed proofs show that the proposed scheme is of unconditional security. Since the secret is shared among three participants, the proposed scheme may be applied to quantum key distribution and secret sharing.     

Quantum Secret Sharing with Two-Particle Entangled States

We present a new protocol for the quantum secret sharing （QSS） task among multiparties with two-particle entangled states. In our scheme, the secret is split among a number of participatlng partners and the reconstruction requires collaboration of all the authorized partners. Instead of multiparticle Greenberger-Horne-Zeillnger states, only two-particle entangled states are employed in this scheme. By local operations and individual measurements on either of the two entangled particles, each authorized partner obtains a sequence of secret bits shared with other authorized partners. This protocol can be experimentally realized using only linear optical elements and simple entanglement source. It is scalable in practice.     

束缚纠缠态量子秘密共享的不安全性分析

分析了以Smolin束缚纠缠态作为通道量子态的量子秘密共享方案的安全性.给出了一个简单的来自通信方内部的截获重发攻击策略,这个攻击策略是依赖比对单量子比特测量结果的窃听检测程序所不能检测出来的.结果表明,仅以束缚纠缠Smolin态作为通道量子态的量子秘密共享方案对于来自内部的窃听攻击不是无条件的.     

Multi-party d-Level Quantum Secret Sharing Scheme

We develop a multiparty quantum secret sharing (QSS) scheme of classical messages based on arbitrary dimensional multi-particle Greenberger-Horne-Zeilinger (GHZ) states. This scheme can be implemented using only local operations, e.g. generalized Z gate and Hadamard gate, and classical communication (LOCC) between participants. The security of the present scheme against exterior eavesdropping and interior dishonest party has been analyzed and confirmed. Moreover, we discuss the possibility of successful sharing of classical messages in the realistic situation where our QSS scheme is carried out in generalized Pauli channels.     

Multiparty Quantum Secret Sharing of Quantum States with Quantum Registers

A quantum secret sharing scheme is proposed by making use of quantum registers. In the proposed scheme, secret message state is encoded into multipartite entangled states. Several identical multi-particle entanglement states are generated and each particle of the entanglement state is filled in different quantum registers which act as shares of the secret message. Two modes, i.e. the detecting mode and the message mode, are employed so that the eavesdropping can be detected easily and the secret message may be recovered. The security analysis shows that the proposed scheme is secure against eavesdropping of eavesdropper and cheating of participants.     

Scalable Quantum Secret Sharing Extended from Quantum Key Distribution

We suggest a general approach for extending quantum key distribution （Q, KD） protocols possessing discrete rotational symmetry into quantum secret sharing （QSS） schemes among multiparty, under certain conditions. Only local unitary operations are required for this generalization based on the almost mature technologies of Q, KD. Theoretically, the number of the participating partners can be arbitrary high. As an application of this method, we propose a fault-tolerant QSS protocol based on a fault-tolerant QKD implementation. The 6-state protocol is also discussed.     

Quantum multicast schemes of different quantum states via non-maximally entangled channels with multiparty involvement

Due to the unavoidable interaction between the quantum channel and its ambient environment, it is difficult to generate and maintain the maximally entanglement. Thus, the research on multiparty information transmission via non-maximally entangled channels is of academic value and general application. Here, we utilize the non-maximally entangled channels to implement two multiparty remote state preparation schemes for transmitting different quantum information from one sender to two receivers synchronously. The first scheme is adopted to transmit two different four-qubit cluster-type entangled states to two receivers with a certain probability. In order to improve success probabilities of such multicast remote state preparation using non-maximally entangled channels, we put forward the second scheme, which deals with the situation that is a synchronous transfer of an arbitrary single-qubit state and an arbitrary two-qubit state from one sender to two receivers. In particular, its success probability can reach 100% in principle, and independent of the entanglement degree of the shared non-maximally entangled channel. Notably, in the second scheme, the auxiliary particle is not required.     

Measurement-device-independent quantum secret sharing with hyper-encoding

Quantum secret sharing (QSS) is a typical multi-party quantum communication mode, in which the key sender splits a key into several parts and the participants can obtain the key by cooperation. Measurement-device-independent quantum secret sharing (MDI-QSS) is immune to all possible attacks from measurement devices and can greatly enhance QSS's security in practical applications. However, previous MDI-QSS's key generation rate is relatively low. Here, we adopt the polarization-spatial-mode hyper-encoding technology in the MDI-QSS, which can increase single photon's channel capacity. Meanwhile, we use the cross-Kerr nonlinearity to realize the complete hyper-entangled Greenberger—Horne—Zeilinger state analysis. Both above factors can increase MDI-QSS's key generation rate by about 10³. The proposed hyper-encoded MDI-QSS protocol may be useful for future multiparity quantum communication applications.     

Multiparty Quantum Secret Sharing of Quantum States Using Entanglement States

A multi-partite-controlled quantum secret sharing scheme using several non-orthogonal entanglement states is presented with unconditional security. In this scheme, the participants share the secret quantum state by exchanging the secret polarization angles of the disordered travel particles. The security of the secret quantum state is also guaranteed by the non-orthogonal multi-partite-controlled entanglement states, the participants＇ secret polarizations, and the disorder of the travelling particles. Moreover, the present scheme is secure against the particle-number splitting attack and the intercept-and-resend attack. It may be still secure even if the distributed quantum state is embedded in a not-so-weak coherent-state pulse.     

An enhancement on Shi et al.'s multiparty quantum secret sharing protocol

Recently, Shi et al. proposed a multiparty quantum secret sharing (QSS) using Bell states and Bell measurements. In their protocol, for sharing two classical bits, all parties have to possess two photons after entanglement swapping. This paper proposes an enhancement of Shi et al.'s protocol. Based on the idea that all parties (except dealer) possess two photons to share two classical bits, the qubit efficiency has further improved by removing the photons the dealer has to hold in Shi et al.'s protocol. Moreover, an insider attack is also prevented in the proposed scheme.     

Quantum key distribution protocol using dense coding of three-qubit W state

The three-qubit W state, with an important feature that each pair of it’s qubits has the same and maximum amount of bipartite entanglement, can be reduced to an entangled 2-qubit system if one of its qubits is lost. Recently, Xue et al. proposed a three-party quantum secret sharing (QSS) protocol based on the three-qubit W state [Chinese Phys. 15, 7 (2006)]. Also, Joo et al. proposed a pair-wise quantum key distribution protocol among three users based on a special measurement on the three-qubit W state [eprint arXiv:quant-ph/0204003v2 (2002)]. This study aims to propose a novel quantum key distribution protocol (QKDP) for arbitrary two communications based on the dense coding and the special measurement of three-qubit W state with the X basis and the Z basis.     

Experimental demonstration of four-party quantum secret sharing

Secret sharing is a multiparty cryptographic task in which some secret information is split into several pieces which are distributed among the participants such that only an authorized set of participants can reconstruct the original secret. Similar to quantum key distribution, in quantum secret sharing, the secrecy of the shared information relies not on computational assumptions, but on laws of quantum physics. Here, we present an experimental demonstration of four-party quantum secret sharing via the resource of four-photon entanglement.