arXiv subjects

L. Magnin

Publications and source records attributed to L. Magnin.

3 recordsLinked to original sources

arXiv2010

Two examples about zero torsion linear maps on Lie algebras

The question of whether or not any zero torsion linear map on a non abelian real Lie algebra g is necessarily an extension of some CR-structure is considered and answered in the negative. Two examples are provided, one in the negative and one in the positive.In both cases, the computation up to equivalence of all zero torsion linear maps on g is used for an explicit description of the equivalence classes of integrable complex structures on the direct product g x g.

math.RA↗

arXiv2007

Heisenberg-limited eavesdropping on the continuous-variable quantum cryptographic protocol with no basis switching is impossible

The Gaussian quantum key distribution protocol based on coherent states and heterodyne detection [Phys. Rev. Lett. 93, 170504 (2004)] has the advantage that no active random basis switching is needed on the receiver's side. Its security is, however, not very satisfyingly understood today because the bounds on the secret key rate that have been derived from Heisenberg relations are not attained by any known scheme. Here, we address the problem of the optimal Gaussian individual attack against this protocol, and derive tight upper bounds on the information accessible to an eavesdropper. The optical scheme achieving this bound is also exhibited, which concludes the security analysis of this protocol.

quant-ph↗

arXiv2004

Complex structures on indecomposable 6-dimensional nilpotent real Lie algebras

We compute all complex structures on indecomposable 6-dimensional real Lie algebras and their equivalence classes. We also give for each of them a global holomorphic chart on the connected simply connected Lie group associated to the real Lie algebra and write down the multiplication in that chart.

math.RA↗