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

Verifiable nonlinear quantum evolution implies failure of density matrices to represent proper mixtures