  In this paper we study the Fisher information metric on the space of the
coupling constants on both sides of the duality between non-relativistic dipole
field theories and string theory in Schr\"odinger spacetime. We consider the
following setup. In the gauge theory side one can deform a given conformal
field theory by a proper scalar operator and compute the quantum information
metric via the two-point correlation function between two such operators. On
the string side the deformation corresponds to a scalar field probing the
background. In the large $N$ limit of the theory the probing can be done
without backreaction on the original spacetime, thus one can construct a
perturbative scheme for the calculation of the dual holographic Fisher
information metric as shown by \cite{Trivella:2016brw}. Considering the
asymptotic behaviour of the holographic Fisher information metric close to the
boundary of the Schr\"odinger spacetime we show that its divergence structure
exactly matches its dual quantum counterpart up to the leading order, thus
extending the holographic setup up to the non-relativistic case. One should
note that the existence of other terms are not seen from the boundary theory to
this level of approximation. Their behaviour near the boundary however, is
pointing what kind of information from the boundary theory is missing to be
able to reconstruct the bulk. Obviously more work is needed to refine and
elucidate their meaning and interrelations in holographic setup.
