  Passive environment assisted communication takes place via a quantum channel
modeled as a unitary interaction between the information carrying system and an
environment, where the latter is controlled by a passive helper, who can set
its initial state such as to assist sender and receiver, but not help actively
by adjusting her behaviour depending on the message. Here we investigate the
information transmission capabilities in this framework by considering Gaussian
unitaries acting on Bosonic systems.
  We consider both quantum communication and classical communication with
helper, as well as classical communication with free classical coordination
between sender and helper (conferencing encoders).
  Concerning quantum communication, we prove general coding theorems with and
without energy constraints, yielding multi-letter (regularized) expressions.
  In the search for cases where the capacity formula is computable, we look for
Gaussian unitaries that are universally degradable or anti-degradable. However,
we show that no Gaussian unitary yields either a degradable or anti-degradable
channel for all environment states. On the other hand, restricting to Gaussian
environment states, results in universally degradable unitaries, for which we
thus can give single-letter quantum capacity formulas.
  Concerning classical communication, we prove a general coding theorem for the
classical capacity under and energy constraint, given by a multi-letter
expression. Furthermore, we derive an uncertainty-type relation between the
classical capacities of the sender and the helper, helped respectively by the
other party, showing a lower bound on the sum of the two capacities. Then, this
is used to lower bound the classical information transmission rate in the
scenario of classical communication between sender and helper.
