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We study the power of closed timelike curves (CTCs) and other nonlinearextensions of quantum mechanics for distinguishing nonorthogonal states andspeeding up hard computations. If a CTC-assisted computer is presented with alabeled mixture of states to be distinguished--the most natural formulation--weshow that the CTC is of no use. The apparent contradiction with recent claimsthat CTC-assisted computers can perfectly distinguish nonorthogonal states isresolved by noting that CTC-assisted evolution is nonlinear, so the output ofsuch a computer on a mixture of inputs is not a convex combination of itsoutput on the mixture's pure components. Similarly, it is not clear that CTCassistance or nonlinear evolution help solve hard problems if computation isdefined as we recommend, as correctly evaluating a function on a labeledmixture of orthogonal inputs.

Can closed timelike curves or nonlinear quantum mechanics improve quantum state discrimination or help solve hard problems?