Robust Interior Point Method for Quantum Key Distribution Rate Computation

Abstract

Security proof methods for quantum key distribution, QKD, that are based on the numerical key rate calculation problem, are powerful in principle. However, the practicality of the methods are limited by computational resources and the efficiency and accuracy of the underlying algorithms for convex optimization. We derive a stable reformulation of the convex nonlinear semidefinite programming, SDP, model for the key rate calculation problems. We use this to develop an efficient, accurate algorithm. The stable reformulation is based on novel forms of facial reduction, FR, for both the linear constraints and nonlinear quantum relative entropy objective function. This allows for a Gauss-Newton type interior-point approach that avoids the need for perturbations to obtain strict feasibility, a technique currently used in the literature. The result is high accuracy solutions with theoretically proven lower bounds for the original QKD from the FR stable reformulation. This provides novel contributions for FR for general SDP. We report on empirical results that dramatically improve on speed and accuracy, as well as solving previously intractable problems.

Security of quantum key distribution from generalised entropy accumulation

“…refs. 6 , 7 , 13 , 49 , 50 ). The key difficulty is that we need a lower bound on the infimum of a concave function .…”

A Swarming Meyer Wavelet Computing Approach to Solve the Transport System of Goods

“…It is utilized in order to produce speedy results by applying the original data of PSO. Recently, the interior-point approach has been functional in quantum key distribution rate computation [32], facility layout problems with relative-positioning constraints [33], nonsymmetric exponentialcone optimization [34], nonlinear forms of the third kind of multi-singular differential system [35], and alternating current optimal power flow [36].…”