  Rapid miniaturization of electronic devices and circuits demands profound
understanding of fluctuation phenomena at the nanoscale. Superconducting
nanowires -- serving as important building blocks for such devices -- may
seriously suffer from fluctuations which tend to destroy long-range order and
suppress superconductivity. In particular, quantum phase slips (QPS)
proliferating at low temperatures may turn a quasi-one-dimensional
superconductor into a resistor or an insulator. Here, we introduce a physical
concept of QPS-controlled localization of Cooper pairs that may occur even in
uniform nanowires without any dielectric barriers being a fundamental
manifestation of the flux-charge duality in superconductors. We demonstrate --
both experimentally and theoretically -- that deep in the "insulating" state
such nanowires actually exhibit non-trivial superposition of superconductivity
and weak Coulomb blockade of Cooper pairs generated by quantum tunneling of
magnetic fluxons across the wire.
