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Obtaining insight into the constituents of dark matter and their interactions with normal matter has inspired a wide range of experimental efforts. Several approaches, particularly those involving searches for ultralight bosonic dark matter (UBDM) fields, involve the use of quantum systems or measurements performed at the limits imposed by quantum mechanics. While a classical treatment of UBDM and its detectors is satisfactory, a fully quantum description would assist in developing future detection strategies. Here, we present an open quantum systems approach that accomplishes this while providing intuition into the quantum nature of the detection process itself. Furthermore, we apply the quantum theory of optical coherence to characterize the statistical properties of the UBDM field. Using representative examples, we show that this theoretical treatment has implications in uncovering signatures of the cosmological production mechanism of the UBDM field and its galactic merger history. By adapting tools from quantum optics, this work will help facilitate the creation of novel methods to extract astrophysically relevant information from correlation measurements. Published by the American Physical Society2025