  We revisit a method for mapping arbitrary single-mode pure states into
superpositions of N00N states using an asymmetric non-linear Mach-Zehnder
interferometer (ANLMZI). This method would allow for one to tailor-make
superpositions of N00N states where each axis of the two-mode joint-photon
number distribution is weighted by the statistics of any single-mode pure
state. The non-linearity of the ANLMZI comes in the form of a
$\chi^{\left(3\right)}$ self-Kerr interaction occurring on one of the
intermediary modes of the interferometer. Motivated by the non-classical
interference effects that occur at a beam splitter, we introduce
inverse-engineering techniques aimed towards extrapolating optimal
transformations for generating N00N state superpositions. These techniques are
general enough so as to be employed to probe the means of generating states of
any desired quantum properties.
