  The quantum Cheshire cat (QCC) thought experiment proposes that a quantum
object's property (\textit{e.g} polarisation, spin, etc.) can be separated from
its physical body or \textit{disembodied}. This conclusion arose from an
argument that interprets a zero weak value (WV) of polarisation as no
polarisation. We show that this argument is incomplete in the sense that a zero
WV reading could equally be interpreted as linear polarisation. Nevertheless,
through a generalisation of the QCC, we complete their argument by excluding
the possibility of linear polarisation as a consistent interpretation. We go
further, and introduce the dual of the generalised QCC. The dual QCC exhibits
an intriguing effect, where a horizontally-polarised interferometer with just
one arm, can give rise to interference which is vertically-polarised. The
interference appears to arise as the result of the phase difference between the
physical arm and a \textit{phantom} arm. This peculiar effect arises from the
interplay between the pre-selected and post-selected states, which
characterises WVs. The QCC has not yet been unambiguously experimentally
demonstrated. The QCC dual offers an alternative pathway to experimental
realisation.
