Q-deformation, discrete time and quantum information as fiber space

In this paper we show the connection between the q-deformation and discrete time, starting from the q-deformed Heisenberg uncertainty relation and q-deformation calculus. We show that time has discrete nature and for this case we construct the connection between quantum information and spacetime via fiber space structure. 1 Heisenberg uncertainty relation, q-deformation and discretization of spacetime Following the papers [1] let observables Q and P fulfill: a = 1/ √ 2(Q+ iP) , a = 1/ √ 2(Q− iP) (1) where a and a are creation and anihilation operators as usual and [Q,P] = i. We shall define △P ≡ P − 〈P 〉 and △Q ≡ Q − 〈Q〉 . Then the famous Heisenberg uncertainty relation for observables Q and P : 1 2 |〈[Q,P]〉| = 1 2 |〈[△Q,△P]〉| ≤ 〈△Q〉 1 2 〈△P〉 12 . (2)