ua nt - p h / 03 03 17 5 v 1 2 9 M ar 2 00 3 Shor ’ s Algorithm for Factoring Large Integers ∗

ua nt - p h / 03 06 19 6 v 1 2 9 Ju n 20 03 On Shor ’ s channel extension and constrained channels

ua nt - p h / 03 03 12 0 v 1 1 9 M ar 2 00 3 Maths - type q - deformed coherent states for q > 1

Maths-type q-deformed coherent states with q > 1 allow a resolution of unity in the form of an ordinary integral. They are sub-Poissonian and squeezed. They may be associated with a harmonic oscillator with minimal uncertainties in both position and momentum and are intelligent coherent states for the corresponding deformed Heisenberg algebra.

ar X iv : q ua nt - p h / 03 09 02 9 v 1 2 S ep 2 00 3 Rule ( 4 ) and Continuous Observation Richard

The effect of rule (4) on a series or parallel sequence of quantum mechanical steps is to insure that a conscious observer does not skip a step. This rule effectively places the observer in continuous contact with the system.

ar X iv : q ua nt - p h / 04 06 14 5 v 2 1 3 A ug 2 00 5 A precise estimation of the computational complexity in Shor ’ s factoring algorithm

P.W.Shor proposed the algorithm to solve the factorization into prime factors within polynomial time by using the quantum computer [1, 2]. See also [5], on the recent advances of the Shor’s factoring algorithm. In his paper, the number of the computational steps was estimated. Through this paper, we consider the case that we factorize n into finite prime numbers pi, (i = 1, · · · , k). We deriv...

ua nt - p h / 05 03 04 1 v 1 3 M ar 2 00 5 Differential geometry of density states

We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.