  We demonstrate symmetric wave propagations in asymmetric nonlinear quantum
systems. By solving the nonlinear Sch\"ordinger equation, we first analytically
prove the existence of symmetric transmission in asymmetric systems with a
single nonlinear delta-function interface. We then point out that a finite
width of the nonlinear interface region is necessary to produce non-reciprocity
in asymmetric systems. However, a geometrical resonant condition for breaking
non-reciprocal propagation is then identified theoretically and verified
numerically. With such a resonant condition, the nonlinear interface region of
finite width behaves like a single nonlinear delta-barrier so that wave
propagations in the forward and backward directions are identical under
arbitrary incident wave intensity. As such, reciprocity re-emerges periodically
in the asymmetric nonlinear system when changing the width of interface region.
Finally, similar resonant conditions of discrete nonlinear Sch\"ordinger
equation are discussed. Therefore, we have identified instances of Reciprocity
Theorem that breaking spatial symmetry in nonlinear interface systems is not
sufficient to produce non-reciprocal wave propagation.
