  In a recent Letter, Bennett and coworkers [1] argue that proofs of exotic
quantum effects using closed timelike curves (CTC's) based on the work of
Deutsch [2], or other nonlinear quantum dynamics, suffer from a fallacy that
they call the "linearity trap," by which one cannot assume that a classical
mixture of input states will lead to the same mixture of corresponding output
states. We show that this prescription is inconsistent with the assumption that
one can verify the postulated nonlinear evolution. Specifically, if some agent
can empirically verify the deterministic nonlinear action of a physical device
for some set of pure-state inputs, then one cannot generally use density
matrices to represent the input for a second agent who is ignorant of the
actual pure state prepared. Our argument is epistemological and makes no appeal
to the detailed physics of CTC's.
