Computing the key rate in quantum distribution (QKD) protocols is a long standing challenge. Analytical methods are limited to handful of with highly symmetric measurement bases. Numerical can handle arbitrary bases, but either use min-entropy, which gives loose lower bound von Neumann entropy, or rely on cumbersome dedicated algorithms. Based recently discovered semidefinite programming (SDP) ...

Considering that preprocessing is an important phase in linear programming, it should be systematically more incorporated in semidefinite programming solvers. The conversion method proposed by the authors (SIAM Journal on Optimization, vol. 11, pp. 647–674, 2000, and Mathematical Programming, Series B, vol. 95, pp. 303–327, 2003) is a preprocessing of sparse semidefinite programs based on matri...

This paper presents semidefinite programming approaches for computing confidential bounds for the dynamic steady-state responses of a damped structure subjected to uncertain driving loads. We assume that amplitudes of harmonic driving loads obey a non-probabilistic uncertainty model. The semidefinite programming problems are formulated for finding confidential bounds for various characteristic ...

This paper presents semidefinite programming approaches for computing confidential bounds for the dynamic steady-state responses of a damped structure subjected to uncertain driving loads. We assume that amplitudes of harmonic driving loads obey a non-probabilistic uncertainty model. The semidefinite programming problems are formulated for finding confidential bounds for various characteristic ...

In this paper we define semidefinite packing programs and describe an algorithm to approximately solve these problems. Semidefinite packing programs arise in many applications such as semidefinite programming relaxations for combinatorial optimization problems, sparse principal component analysis, and sparse variance unfolding techniques for dimension reduction. Our algorithm exploits the struc...