  The theory of linear quantum measurement has been developed for analysing the
sensitivities of experimental devices that measure extremely weak signals, such
as gravitational waves. It has successfully contributed to the theoretical
understanding of laser interferometer gravitational-wave detectors (used by
LIGO, VIRGO and KaGRA) and helped many important experimental upgrades. In this
work, we establish a linear quantum measurement theory for another kind of
measurement device--- matter wave interferometers, which has been widely
discussed as an important platform for many high-precision experiments. This
theory allows us to account for both atom and light fluctuations, and leads to
a detailed analysis of back-action in matter-wave interferometry (action of
light back onto the atoms) and its effect on dynamics and measurement noise.
From this analysis, we obtain a Standard Quantum Limit (SQL) for matter-wave
interferometry. A comparison between the LIGO detector and matter wave
interferometer is also given from the perspective of quantum measurement.
