Numerical simulation of the optimal two-mode attacks for two-way continuous-variable quantum cryptography in reverse reconciliation

We analyze the security of the two-way continuous-variable quantum key distribution protocol in reverse reconciliation against general two-mode attacks, which represent all accessible attacks at fixed channel parameters. Rather than against one specific attack model, the expression of secret key rates of the two-way protocol are derived against all accessible attack models. It is found that there is an optimal two-mode attack to minimize the performance of the protocol in terms of both secret key rates and maximal transmission distances. We identify the optimal two-mode attack, give the specific attack model of the optimal two-mode attack and show the performance of the two-way protocol against the optimal two-mode attack. Even under the optimal two-mode attack, the performances of two-way protocol are still better than the corresponding one-way protocol, which shows the advantage of making a double use of the quantum channel and the potential of long-distance secure communication using two-way protocol.Comment: 14 pages, 8 figure

Improvement of two-way continuous-variable quantum key distribution with virtual photon subtraction

We propose a method to improve the performance of two-way continuous-variable quantum key distribution protocol by virtual photon subtraction. The Virtual photon subtraction implemented via non-Gaussian post-selection not only enhances the entanglement of two-mode squeezed vacuum state but also has advantages in simplifying physical operation and promoting efficiency. In two-way protocol, virtual photon subtraction could be applied on two sources independently. Numerical simulations show that the optimal performance of renovated two-way protocol is obtained with photon subtraction only used by Alice. The transmission distance and tolerable excess noise are improved by using the virtual photon subtraction with appropriate parameters. Moreover, the tolerable excess noise maintains a high value with the increase of distance so that the robustness of two-way continuous-variable quantum key distribution system is significantly improved, especially at long transmission distance.Comment: 15 pages, 6 figure

Optimum Combination of Insulin-Transferrin-Selenium and Fetal Bovine Serum for Culture of Rabbit Articular Chondrocytes in Three-Dimensional Alginate Scaffolds

Fetal bovine serum (FBS) has been reported to affect chondrocyte biosynthesis in monolayer culture. Insulin-Transferrin-Selenium (ITS) was investigated as a partial replacement for FBS during in vitro culture of rabbit articular chondrocytes in three-dimensional alginate scaffold. Chondrocyte-seeded alginate hydrogels were cultured in Dulbecco's modified Eagle's medium plus 10% FBS, 1% ITS plus 2% FBS, 1% ITS plus 4% FBS, or 1% ITS plus 8% FBS. At designed time point, the Chondrocyte-seeded alginate hydrogels were harvested and evaluated with histological staining, immunohistochemistry, and quantitative gene expression analysis. Viable cell density and cell division were also evaluated. Chondrocytes biosynthesis and cell division in 1% ITS with 2% FBS medium were similar to that in medium added with 10% FBS. For a total culture of 3 weeks, phenotypic gene expression in chondrocyte-seeded hydrogels was maintained at high levels in medium with 1% ITS plus 2% FBS, while it was decreased to varying degrees in the other groups. In conclusion, with 1% ITS, medium with 2% FBS could promote chondrocyte biosynthesis and cell division, and prevented cell dedifferentiation in three-dimensional alginate scaffolds

Finite-size analysis of continuous-variable measurement-device-independent quantum key distribution

We study the impact of the finite-size effect on the continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocol, mainly considering the finite-size effect on the parameter estimation procedure. The central-limit theorem and maximum likelihood estimation theorem are used to estimate the parameters. We also analyze the relationship between the number of exchanged signals and the optimal modulation variance in the protocol. It is proved that when Charlie's position is close to Bob, the CV-MDI QKD protocol has the farthest transmission distance in the finite-size scenario. Finally, we discuss the impact of finite-size effects related to the practical detection in the CV-MDI QKD protocol. The overall results indicate that the finite-size effect has a great influence on the secret key rate of the CV-MDI QKD protocol and should not be ignored.Comment: 9 pages, 9 figure

Continuous and discontinous compressible flows in a converging-diverging channel solved by physics-informed neural networks without data

Physics-informed neural networks (PINNs) are employed to solve the classical compressible flow problem in a converging-diverging nozzle. This problem represents a typical example described by the Euler equations, thorough understanding of which serves as a guide for solving more general compressible flows. Given a geometry of the channel, analytical solutions for the steady states indeed exist and they depend on the ratio between the back pressure of the outlet and stagnation pressure of the inlet. Moreover, in the diverging region, the solution may branch into subsonic flow, supersonic flow, and a mixture of both with a discontinuous transition where a normal shock takes place. Classical numerical schemes with shock-fitting/capturing methods have been designed to solve this type of problem effectively, whereas the original PINNs fail in front of the hyperbolic non-linear partial differential equations. We make a first attempt to exploit the power of PINNs to directly solve this problem by adjusting the weights of different components of the loss function, to acquire physical solutions and meanwhile avoid trivial solutions. With a universal setting yet no exogenous data, we are able to solve this problem accurately, that is, for different given pressure ratios PINNs provide different branches of solutions at both steady and unsteady states, some of which are discontinuous in nature