  Despite well-established no-go theorems on a perfect linear optical Bell
state analyzer, we find a numerical trend that appears to approach a
near-perfect measurement if we incorporate eight or more un-entangled ancilla
photons into our device. Following this trend, we begin a promising inductive
approach to building an ideal optical Bell measurement device. In the process,
we determine that any Bell state analyzer that (even occasionally) bunches all
photons into only two of the output modes cannot perform an ideal measurement
and we find a set of conditions on our linear optical circuit that prevent this
outcome.
