  One of the most promising applications of quantum networks is entanglement
assisted sensing. The field of quantum metrology exploits quantum correlations
to improve the precision bound for applications such as precision timekeeping,
field sensing, and biological imaging. When measuring multiple spatially
distributed parameters, current literature focuses on quantum entanglement in
the discrete variable case, and quantum squeezing in the continuous variable
case, distributed amongst all of the sensors in a given network. However, it
can be difficult to ensure all sensors pre-share entanglement of sufficiently
high fidelity. This work probes the space between fully entangled and fully
classical sensing networks by modeling a star network with probabilistic
entanglement generation that is attempting to estimate the average of local
parameters. The quantum Fisher information is used to determine which protocols
best utilize entanglement as a resource for different network conditions. It is
shown that without entanglement distillation there is a threshold fidelity
below which classical sensing is preferable. For a network with a given number
of sensors and links characterized by a certain initial fidelity and
probability of success, this work outlines when and how to use entanglement,
when to store it, and when it needs to be distilled.
