  We study the feasibility of sub-shot-noise interferometry with imperfect
detectors, starting from twin-Fock states and two mode squeezed vacuum states.
We derive analytical expressions for the corresponding phase uncertainty. We
find that one can achieve phase shift measurements below the standard quantum
limit, as long as the losses are smaller than a given threshold, and that the
measured phase is close enough to an optimal value. We provide our analytical
formulae in a Python package, accessible online.
