  We establish a framework for oracle identification problems in the continuous
variable setting, where the stated problem necessarily is the same as in the
discrete variable case, and continuous variables are manifested through a
continuous representation in an infinite-dimensional Hilbert space. We apply
this formalism to the Deutsch-Jozsa problem and show that, due to an
uncertainty relation between the continuous representation and its
Fourier-transform dual representation, the corresponding Deutsch-Jozsa
algorithm is probabilistic hence forbids an exponential speed-up, contrary to a
previous claim in the literature.
