  We present a quantum model which provides enhanced understanding of recent
transverse magnetic focusing experiments on graphene $p$-$n$ junctions.
Spatially resolved flow maps of local particle current density show quantum
interference and $p$-$n$ junction filtering effects which are crucial to
explaining the device operation. The Landauer-B\"{u}ttiker formula is used
alongside dephasing edge contacts to give exceptional agreement between
simulated non-local resistance and the recent experiment by Chen $\textit{et
al}$ ($\textit{Science}$, 2016). The origin of positive and negative focusing
resonances and off resonance characteristics are explained in terms of quantum
transmission functions. Our model also captures subtle features from
experiment, such as the previously unexplained $p$-$p^-$ to $p$-$p^+$
transition and the second $p$-$n$ focusing resonance.
