  We prove that several known upper bounds on the classical capacity of thermal
and additive noise bosonic channels are actually strong converse rates. Our
results strengthen the interpretation of these upper bounds, in the sense that
we now know that the probability of correctly decoding a classical message
rapidly converges to zero in the limit of many channel uses if the
communication rate exceeds these upper bounds. In order for these theorems to
hold, we need to impose a maximum photon number constraint on the states input
to the channel (the strong converse property need not hold if there is only a
mean photon number constraint). Our first theorem demonstrates that Koenig and
Smith's upper bound on the classical capacity of the thermal bosonic channel is
a strong converse rate, and we prove this result by utilizing the structural
decomposition of a thermal channel into a pure-loss channel followed by an
amplifier channel. Our second theorem demonstrates that Giovannetti et al.'s
upper bound on the classical capacity of a thermal bosonic channel corresponds
to a strong converse rate, and we prove this result by relating success
probability to rate, the effective dimension of the output space, and the
purity of the channel as measured by the Renyi collision entropy. Finally, we
use similar techniques to prove that similar previously known upper bounds on
the classical capacity of an additive noise bosonic channel correspond to
strong converse rates.
