Efficient quantum private comparison protocol based on one direction discrete quantum walks on the circle

We propose an efficient quantum private comparison protocol firstly based on one direction quantum walks. With the help of one direction quantum walk, we develop a novel method that allows the semi-honest third party to set a flag to judge the comparing result, which improves the qubit efficiency and the maximum quantity of the participants' secret messages. Besides, our protocol can judge the size of the secret messages, not only equality. Furthermore, the quantum walks particle is disentangled in the initial state. It only requires a quantum walks operator to move, making our proposed protocol easy to implement and reducing the quantum resources. Through security analysis, we prove that our protocol can withstand well-known attacks and brute-force attacks. Analyses also reveal that our protocol is correct and practical.     

Quantum multicast communication over the butterfly network

We propose a scheme where one can exploit auxiliary resources to achieve quantum multicast communication with network coding over the butterfly network.In this paper,we propose the quantum 2-pair multicast communication scheme,and extend it to k-pair multicast communication over the extended butterfly network.Firstly,an EPR pair is shared between each adjacent node on the butterfly network,and make use of local operation and classical communication to generate entangled relationship between non-adjacent nodes.Secondly,each sender adds auxiliary particles according to the multicast number k,in which the CNOT operations are applied to form the multi-particle entangled state.Finally,combined with network coding and free classical communication,quantum multicast communication based on quantum measurements is completed over the extended butterfly network.Not only the bottleneck problem is solved,but also quantum multicast communication can be completed in our scheme.At the same time,regardless of multicast number k,the maximum capacity of classical channel is 2 bits,and quantum channel is used only once.     

Efficient quantum private comparison protocol utilizing single photons and rotational encryption

As a branch of quantum secure multiparty computation, quantum private comparison is applied frequently in many fields, such as secret elections, private voting, and identification. A quantum private comparison protocol with higher efficiency and easier implementation is proposed in this paper. The private secrets are encoded as single polarized photons and then encrypted with a homomorphic rotational encryption method. Relying on this method and the circular transmission mode, we implement the multiplexing of photons, raising the efficiency of our protocol to 100%. Our protocol is easy to realize since only single photons, unitary operation, and single-particle measurement are introduced. Meanwhile, the analysis shows that our protocol is also correct and secure.     

Constructing the three-qudit unextendible product bases with strong nonlocality

Unextendible product bases (UPBs) are interesting members of a family of orthogonal product bases. Here, we investigate the construction of 3-qudit UPBs with strong nonlocality. First, a UPB set in ${{C}^{3}}\otimes {{C}^{3}}\otimes {{C}^{3}}$ of size 19 is presented based on the shift UPBs. By mapping the system to a Rubik's cube, we provide a general method of constructing UPBs in ${{C}^{d}}\otimes {{C}^{d}}\otimes {{C}^{d}}$ of size ${{\left(d-1 \right)}^{3}}+2d+5$, whose corresponding Rubik's cube is composed of four parts. Second, for the more general case where the dimensions of parties are different, we extend the classical tile structure to the 3-qudit system and propose the tri-tile structure. By means of this structure, a ${{C}^{4}}\otimes {{C}^{4}}\otimes {{C}^{5}}$ system of size 38 is obtained based on a ${{C}^{3}}\otimes {{C}^{3}}\otimes {{C}^{4}}$ system of size 19. Then, we generalize this approach to the ${{C}^{{{d}_{1}}}}\otimes {{C}^{{{d}_{2}}}}\otimes {{C}^{{{d}_{3}}}}$ system which also consists of four parts. Our research provides a positive answer to the open question raised in by Halder et al. [$Phys. Rev. Lett$. 122 040403 (2019)], indicating that there do exist UPBs that can exhibit strong quantum nonlocality without entanglement.     

A rational quantum state sharing protocol with semi-off-line dealer

A rational quantum state sharing protocol with the semi-off-line dealer is proposed. Firstly, the dealer Alice shares an arbitrary two-particle entangled state with the players by Einstein-Podolsky-Rosen (EPR) pairs and Greenberger-Horne-Zeilinger (GHZ) states. The EPR pairs are prepared by Charlie instead of the dealer, reducing the workload of the dealer. Secondly, all players have the same probability of reconstructing the quantum state, guaranteeing the fairness of the protocol. In addition, the dealer is semi-off-line, which considerably reduces the information exchanging between the dealer and the players. Finally, our protocol achieves security, fairness, correctness, and strict Nash equilibrium.