We consider a two-dimensional ͑2D͒electron gas residing on the surface of a cylinder of a given radius R in the presence of a parabolic confinement along the axis of the cylinder. In this way the system of electrons forms a closed cylindrical stripe ͑wire͒. Using the local spin-density technique we first consider localization of electrons within of a potential barrier embedded in the wire. Barriers with sharp retangularlike features are populated in steps because of Coulomb blockade. The nature of a single bound state in a short soft barrier ͑quantum point contacts͒ at pinch-off is discussed in terms Coulomb blockade. For a shallow barrier-free wire we retrace the structural transitions at low electron densities from a single chain of localized states to double and triple chains ͑Wigner spin lattices͒. The present system is related to the model of a inhomogeneous quantum wire introduced recently by Güçlü et al. ͓Phys. Rev. B 80, 201302͑R͒ ͑2009͔͒. An important aspect is, however, the present extension into higher electron densities as well as to the low-density regime and the formation of 2D Wigner microlattices.

We show that the non-parabolic confinement potential is responsible for the non-monotonic behavior and sign change of the exciton fine-structure splitting (FSS) in optically active self-assembled quantum dots. This insight is important for the theoretical understanding and practical control by electric fields of the quantum state of the emitted light from a biexciton cascade recombination process. We find that a hard-wall (box) confinement potential leads to a FSS that is in better agreement with experimentally measured FSS than a harmonic potential. We then show that a finite applied electric field can be used to remove the FSS entirely, thus allowing for the creation of maximally entangled photons, being vital to the growing field of quantum communication and quantum key distribution.