  We work out a microscopic theory describing complete statistics of voltage
fluctuations generated by quantum phase slips (QPS) in superconducting
nanowires. We evaluate the cumulant generating function and demonstrate that
shot noise of the voltage as well as the third and all higher voltage cumulants
differ from zero only due to the presence of QPS. In the zero-frequency limit
voltage fluctuations in superconducting nanowires are described by Poisson
statistics just as in a number of other tunneling-like problems. However, at
non-zero frequencies quantum voltage fluctuations in superconducting nanowires
become much more complicated and are not anymore accounted for by Poisson
statistics. In the case of short superconducting nanowires we explicitly
evaluate all finite-frequency voltage cumulants and establish a non-trivial
relation between these cumulants and the current-voltage characteristics of our
system.
