Continuous Variable Quantum Cryptography -- Discussion of Various Realisations with Qudits

Abstract

We expand the recently discussed continuous-variable quantum key distribution scheme of Heid and Luetkenhaus (2006) to qudits with a lossy but noiseless quantum channel. Postselection methods are used. Secret key rates are calculated in the presence of loss for the direct and the reverse reconciliation method. In the case of reverse reconciliation the secret key rate increases with higher dimensions, in the case of direct reconciliation the result is reverse. Several ways of optimising the amplitude are discussed. In a next step the used states are generalised to squeezed states. Again secret key rates are calculated. The last part deals with the dual-homodyne detection which replaces the single-homodyne measurement. Most results are analytical and allow further treatments if the preparation symmetry stays unchanged.