  The curvelet transform is a special type of wavelet transform, which is
useful for estimating the locations and orientations of waves propagating in
Euclidean space. We prove an uncertainty principle that lower-bounds the
variance of these estimates, for radial wave functions in n dimensions.
  As an application of this uncertainty principle, we show the infeasibility of
one approach to constructing quantum algorithms for solving lattice problems,
such as the approximate shortest vector problem (approximate-SVP), and bounded
distance decoding (BDD). This gives insight into the computational
intractability of approximate-SVP, which plays an important role in algorithms
for integer programming, and in post-quantum cryptosystems.
  In this approach to solving lattice problems, one prepares quantum
superpositions of Gaussian-like wave functions centered at lattice points. A
key step in this procedure requires finding the center of each Gaussian-like
wave function, using the quantum curvelet transform. We show that, for any
choice of the Gaussian-like wave function, the error in this step will be above
the threshold required to solve BDD and approximate-SVP.
