  Quantum teleportation is a primitive in several important applications,
including quantum communication, quantum computation, error correction, and
quantum networks. In this work, we propose an optimal test for the performance
of continuous-variable (CV) quantum teleportation in terms of the
energy-constrained channel fidelity between ideal CV teleportation and its
experimental implementation. Work prior to ours considered suboptimal tests of
the performance of CV teleportation, focusing instead on its performance for
particular states, such as ensembles of coherent states, squeezed states, cat
states, etc. Here we prove that the optimal state for testing CV teleportation
is an entangled superposition of twin Fock states. We establish this result by
reducing the problem of estimating the energy-constrained channel fidelity
between ideal CV teleportation and its experimental approximation to a
quadratic program and solving it. As an additional result, we obtain an
analytical solution to the energy-constrained diamond distance between a
photodetector and its experimental approximation. These results are relevant
for experiments that make use of CV teleportation and photodetectors.
