  In this work we analyze two axis twisting in the presence of depolarizing
channel dissipation. We find that spin squeezing is only possible if the
dissipation is parametrically weaker than the squeezing coupling. Squeezing may
be used for meteorologically useful decrease of spin noise but only in the case
where the squeezing occurs before measurement, in the case one squeezes as one
measures one also squeezes the signal thereby making spin squeezing ineffective
for metrological gain. The key mathematical advance made in this work is the
observation that TACT in the presence of depolarizing noise is equivalent to
TACT with reduced polarization and no noise. We find an exponential gain in
signal to noise with the exponent proportional to the ratio between the
squeezing strength and the depolarization rate.
