Abstract
We argue that quantum phase slips (QPS) may generate non-equilibrium voltage fluctuations in superconducting nanowires. In the low frequency limit we evaluate all cumulants of the voltage operator which obey Poisson statistics and show a power law dependence on the external bias. We specifically address quantum shot noise which power spectrum S_Ω may depend non-monotonously on temperature. In the long wire limit S_Ω decreases with increasing frequency Ω and vanishes beyond a threshold value of Ω at T → 0. Our predictions can be directly tested in future experiments with superconducting nanowires.