  We consider position measurements using the cross-correlated output of two
tunnel junction position detectors. Using a fully quantum treatment, we
calculate the equation of motion for the density matrix of the coupled
detector-detector-mechanical oscillator system. After discussing the presence
of a bound on the peak-to-background ratio in a position measurement using a
single detector, we show how one can use detector cross correlations to
overcome this bound. We analyze two different possible experimental
realizations of the cross correlation measurement and show that in both cases
the maximum cross-correlated output is obtained when using twin detectors and
applying equal bias to each tunnel junction. Furthermore, we show how the
double-detector setup can be exploited to drastically reduce the added
displacement noise of the oscillator.
