  Communication over a quantum multiple-access channel (MAC) with cribbing
encoders is considered, whereby Transmitter 2 performs a measurement on a
system that is entangled with Transmitter 1. Based on the no-cloning theorem,
perfect cribbing is impossible. This leads to the introduction of a MAC model
with noisy cribbing. In the causal and non-causal cribbing scenarios,
Transmitter 2 performs the measurement before the input of Transmitter 1 is
sent through the channel. Hence, Transmitter 2's cribbing may inflict a "state
collapse" for Transmitter 1. Achievable regions are derived for each setting.
Furthermore, a regularized capacity characterization is established for robust
cribbing, i.e. when the cribbing system contains all the information of the
channel input. Building on the analogy between the noisy cribbing model and the
relay channel, a partial decode-forward region is derived for a quantum MAC
with non-robust cribbing. For the classical-quantum MAC with cribbing encoders,
the capacity region is determined with perfect cribbing of the classical input,
and a cutset region is derived for noisy cribbing. In the special case of a
classical-quantum MAC with a deterministic cribbing channel, the inner and
outer bounds coincide.
