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Nonlinear modifications to the laws of quantum mechanics have been proposedas a possible way to consistently describe information processing in thepresence of closed timelike curves. These have recently generated controversydue to possible exotic information-theoretic effects, including breakingquantum cryptography and radically speeding up both classical and quantumcomputers. The physical interpretation of such theories, however, is stillunclear. We consider a large class of operationally-defined theories thatcontain "nonlinear boxes" and show that operational verifiability withoutsuperluminal signaling implies a split in the equivalence classes ofpreparation procedures. We conclude that any theory satisfying the aboverequirements is (a) inconsistent unless it contains distinct representationsfor the two different kinds of preparations and (b) incomplete unless it alsocontains a rule for uniquely distinguishing them at the operational level. Werefer to this as the preparation problem for nonlinear theories. In addition toits foundational implications, this work shows that, in the presence ofnonlinear quantum evolution, the security of quantum cryptography and theexistence of other exotic effects remain open questions.

The preparation problem in nonlinear extensions of quantum theory