  The Bekenstein bound posits a maximum entropy for matter with finite energy
confined to a spatial region. It is often interpreted as a fundamental limit on
the information that can be stored by physical objects. In this work, we test
this interpretation by asking whether the Bekenstein bound imposes constraints
on a channel's communication capacity, a context in which information can be
given a mathematically rigorous and operationally meaningful definition. We
study specifically the \emph{Unruh channel} that describes a stationary Alice
exciting different species of free scalar fields to send information to an
accelerating Bob, who is confined to a Rindler wedge and exposed to the noise
of Unruh radiation. We show that the classical and quantum capacities of the
Unruh channel obey the Bekenstein bound that pertains to the decoder Bob. In
contrast, even at high temperatures, the Unruh channel can transmit a
significant number of \emph{zero-bits}, which are quantum communication
resources that can be used for quantum identification and many other primitive
protocols. Therefore, unlike classical bits and qubits, zero-bits and their
associated information processing capability are generally not constrained by
the Bekenstein bound. However, we further show that when both the encoder and
the decoder are restricted, the Bekenstein bound does constrain the channel
capacities, including the zero-bit capacity.
