  One of the most sought-after goals in experimental quantum communication is
the implementation of a quantum repeater. The performance of quantum repeaters
can be assessed by comparing the attained rate with the quantum and private
capacity of direct transmission, assisted by unlimited classical two-way
communication. However, these quantities are hard to compute, motivating the
search for upper bounds. Takeoka, Guha and Wilde found the squashed
entanglement of a quantum channel to be an upper bound on both these
capacities. In general it is still hard to find the exact value of the squashed
entanglement of a quantum channel, but clever sub-optimal squashing channels
allow one to upper bound this quantity, and thus also the corresponding
capacities. Here, we exploit this idea to obtain bounds for any
phase-insensitive Gaussian bosonic channel. This bound allows one to benchmark
the implementation of quantum repeaters for a large class of channels used to
model communication across fibers. In particular, our bound is applicable to
the realistic scenario when there is a restriction on the mean photon number on
the input. Furthermore, we show that the squashed entanglement of a channel is
convex in the set of channels, and we use a connection between the squashed
entanglement of a quantum channel and its entanglement assisted classical
capacity. Building on this connection, we obtain the exact squashed
entanglement and two-way assisted capacities of the $d$-dimensional erasure
channel and bounds on the amplitude-damping channel and all qubit Pauli
channels. In particular, our bound improves on the previous best known squashed
entanglement upper bound of the depolarizing channel.
