  Helicity is a topological invariant that measures the linkage and knottedness
of lines, tubes and ribbons. As such, it has found myriads of applications in
astrophysics and solar physics, in fluid dynamics, in atmospheric sciences, and
in biology. In quantum flows, where topology-changing reconnection events are a
staple, helicity appears as a key quantity to study. However, the usual
definition of helicity is not well posed in quantum vortices, and its
computation based on counting links and crossings of vortex lines can be
downright impossible to apply in complex and turbulent scenarios. We present a
new definition of helicity which overcomes these problems. With it, we show
that only certain reconnection events conserve helicity. In other cases
helicity can change abruptly during reconnection. Furthermore, we show that
these events can also excite Kelvin waves, which slowly deplete helicity as
they interact nonlinearly, thus linking the theory of vortex knots with
observations of quantum turbulence.
