In practice, the security of a Quantum Key Distribution (QKD) system relies not only on quantum mechanical principles, but it also significantly relies on the physical implementation of the protocol. Nowadays, technological detector loopholes of QKD systems have been demonstrated, and some successful attacks that exploit vulnerabilities of the Avalanche Photo Diodes (APD’s) have been performed....

A conjecture of P. Erdos says that the diophantine equation x+y = z has infinitely many solutions with (x,y) — 1 and such that if a prime p divides xyz, then p divides xyz. In this paper, we give a proof of this conjecture. Let k ^ 2 be an integer. A /c-powerful number is a positive integer x with the property that if the prime p divides x, then p divides x (2-powerful numbers were called initi...

We prove that the set of leaves of a holomorphic lamination of codimension one that are tangent to a germ of a holomorphic map is discrete. Let F be a holomorphic lamination of codimension one in an open set V in a complex Banach space B. In this paper, this means that V = W × C, where W is a neighborhood of the origin in some Banach space, and the leaves Lλ of the lamination are disjoint graph...

The transverse momentum of a colour-singlet massive particle produced in a hadronic collision provides important information on perturbative and nonperturbative effects. A process like qq! Z0 corresponds to a p?Z = 0, while higher-order processes provide p? kicks as the Z0 recoils against quarks and gluons. At large p?Z values the bulk of the p? comes from one hard emission, and perturbation th...

The Borel cardinality of the quotient of the power set of the natural numbers by the ideal Z0 of asymptotically zero-density sets is shown to be the same as that of the equivalence relation induced by the classical Banach space c0. We also show that a large collection of ideals introduced by Louveau and Veličkovič, with pairwise incomparable Borel cardinality, are all Borel reducible to c0. Thi...