  Suppose we want to benchmark a quantum device held by a remote party, e.g. by
testing its ability to carry out challenging quantum measurements outside of a
free set of measurements $\mathcal{M}$. A very simple way to do so is to set up
a binary state discrimination task that cannot be solved efficiently by means
of free measurements. If one can find pairs of orthogonal states that become
arbitrarily indistinguishable under measurements in $\mathcal{M}$, in the sense
that the error probability in discrimination approaches that of a random guess,
one says that there is data hiding against $\mathcal{M}$. Here we investigate
data hiding in the context of continuous variable quantum systems. First, we
look at the case where $\mathcal{M}=\mathrm{LOCC}$, the set of measurements
implementable with local operations and classical communication. While previous
studies have placed upper bounds on the maximum efficiency of data hiding in
terms of the local dimension and are thus not applicable to continuous variable
systems, we establish more general bounds that rely solely on the local mean
photon number of the states employed. Along the way, we perform a rigorous
quantitative analysis of the error introduced by the non-ideal
Braunstein-Kimble quantum teleportation protocol, determining how much
squeezing and local detection efficiency is needed in order to teleport an
arbitrary multi-mode local state of known mean energy with a prescribed
accuracy. Finally, following a seminal proposal by Sabapathy and Winter, we
look at data hiding against Gaussian operations assisted by feed-forward of
measurement outcomes, providing the first example of a relatively simple scheme
that works with a single mode only.
