  We extend the definition of entanglement witnesses based on structure factors
to the case in which the position of the scatterers is quantized. This allows
us to study entanglement detection in hybrid systems. We provide several
examples that show how these extra degrees of freedom affect the detection of
entanglement by directly contributing to the measurement statistics. We
specialize the proposed witness operators for a chain of trapped ions. Within
this framework, we show how the collective vibronic state of the chain can act
as an undesired quantum environment and how ions quantum motion can affect the
entanglement detection. Finally, we investigate some specific cases where the
method proposed leads to detection of hybrid entanglement.
