  Recent progress in generating entangled spin states of neutral atoms provides
opportunities to advance quantum sensing technology. In particular,
entanglement can enhance the performance of accelerometers and gravimeters
based on light-pulse atom interferometry. We study the effects of error sources
that may limit the sensitivity of such devices, including errors in the
preparation of the initial entangled state, imperfections in the laser pulses,
momentum spread of the initial atomic wave packet, measurement errors,
spontaneous emission, and atom loss. We determine that, for each of these
errors, the expectation value of the parity operator $\Pi$ has the general
form, $\overline{\langle \Pi \rangle} = \Pi_0 \cos( N \phi )$, where $\phi$ is
the interferometer phase and $N$ is the number of atoms prepared in the
maximally entangled Greenberger--Horne--Zeilinger state. Correspondingly, the
minimum phase uncertainty has the general form, $\Delta\phi = (\Pi_0 N)^{-1}$.
Each error manifests itself through a reduction of the amplitude of the parity
oscillations, $\Pi_0$, below the ideal value of $\Pi_0 = 1$. For each of the
errors, we derive an analytic result that expresses the dependence of $\Pi_0$
on error parameter(s) and $N$, and also obtain a simplified approximate
expression valid when the error is small. Based on the performed analysis,
entanglement-enhanced atom interferometry appears to be feasible with existing
experimental capabilities.
