  The nonorthogonality of coherent states is a fundamental property which
prevents them from being perfectly and deterministically discriminated. To
circumvent this problem, we present an experimentally feasible protocol for the
probabilistic orthogonalisation of a pair of coherent states, independent of
their amplitude and phase. In contrast to unambiguous state discrimination,
successful operation of our protocol is heralded without measuring the states,
such that they remain suitable for further manipulation. As such, the resulting
orthogonalised state may be used for further processing. Indeed, these states
are close approximations of the discrete-variable superposition state
$\frac{1}{\sqrt{2}}\left(|0\rangle \pm |1\rangle\right)$. This feature, coupled
with the non-destructive nature of the operation, is especially useful when
considering superpositions of coherent states: such states are mapped to the
(weakly squeezed) vacuum or single photon Fock state, depending on the phase of
the superposition. Thus this operation may find utility in hybrid
continuous-discrete quantum information processing protocols.
