Physics – Quantum Physics
Scientific paper
2009-08-20
Phys.Rev.Lett.103:170502,2009
Physics
Quantum Physics
4 pages, 3 figures. Final version. Added several references, updated discussion and introduction. Figure 1(b) very much enhanc
Scientific paper
10.1103/PhysRevLett.103.170502
We study the power of closed timelike curves (CTCs) and other nonlinear extensions of quantum mechanics for distinguishing nonorthogonal states and speeding up hard computations. If a CTC-assisted computer is presented with a labeled mixture of states to be distinguished--the most natural formulation--we show that the CTC is of no use. The apparent contradiction with recent claims that CTC-assisted computers can perfectly distinguish nonorthogonal states is resolved by noting that CTC-assisted evolution is nonlinear, so the output of such a computer on a mixture of inputs is not a convex combination of its output on the mixture's pure components. Similarly, it is not clear that CTC assistance or nonlinear evolution help solve hard problems if computation is defined as we recommend, as correctly evaluating a function on a labeled mixture of orthogonal inputs.
Bennett Charles H.
Leung Debbie
Smith Graeme
Smolin John A.
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