Quantum phase slips and voltage fluctuations in superconducting nanowires

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 $S_\Omega$ may depend non-monotonously on temperature. In the long wire limit $S_\Omega$ decreases with increasing frequency $\Omega$ and vanishes beyond a threshold value of $\Omega$ at $T \to 0$. Our predictions can be directly tested in future experiments with superconducting nanowires.