  The hypothetical axion particle (of unknown mass) is a leading candidate for
dark matter (DM). Many experiments search for axions with microwave cavities,
where an axion may convert into a cavity photon, leading to a feeble excess in
the output power of the cavity. Recent work [Nature 590, 238 (2021)] has
demonstrated that injecting squeezed vacuum into the cavity can substantially
accelerate the axion search. Here, we go beyond and provide a theoretical
framework to leverage the benefits of quantum squeezing in a network setting
consisting of many sensor-cavities. By forming a local sensor network, the
signals among the cavities can be combined coherently to boost the axion
search. Furthermore, injecting multipartite entanglement across the cavities --
generated by splitting a squeezed vacuum -- enables a global noise reduction.
We explore the performance advantage of such a local, entangled sensor-network,
which enjoys both coherence between the axion signals and entanglement between
the sensors. Our analyses are pertinent to next-generation DM-axion searches
aiming to leverage a network of sensors and quantum resources in an optimal
way. Finally, we assess the possibility of using a more exotic quantum state,
the Gottesman-Kitaev-Preskill (GKP) state. Despite a constant-factor
improvement in the scan-time relative to a single-mode squeezed-state in the
ideal case, the advantage of employing a GKP state disappears when a practical
measurement scheme is considered.
