  We introduce a new approach to evaluating entangled quantum networks using
information geometry. Quantum computing is powerful because of the enhanced
correlations from quantum entanglement. For example, larger entangled networks
can enhance quantum key distribution (QKD). Each network we examine is an
n-photon quantum state with a degree of entanglement. We analyze such a state
within the space of measured data from repeated experiments made by n observers
over a set of identically-prepared quantum states -- a quantum state
interrogation in the space of measurements. Each observer records a 1 if their
detector triggers, otherwise they record a 0. This generates a string of 1's
and 0's at each detector, and each observer can define a binary random variable
from this sequence. We use a well-known information geometry-based measure of
distance that applies to these binary strings of measurement outcomes, and we
introduce a generalization of this length to area, volume and
higher-dimensional volumes. These geometric equations are defined using the
familiar Shannon expression for joint and mutual entropy. We apply our approach
to three distinct tripartite quantum states: the GHZ state, the W state, and a
separable state P. We generalize a well-known information geometry analysis of
a bipartite state to a tripartite state. This approach provides a novel way to
characterize quantum states, and it may have favorable scaling with increased
number of photons.
