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

TL;DR

This paper investigates whether closed timelike curves (CTCs) and nonlinear quantum mechanics can enhance quantum state discrimination or computational complexity, concluding they do not provide advantages in the natural formulations.

Contribution

It clarifies the limitations of CTC-assisted quantum computation and nonlinear evolutions in state discrimination and solving hard problems, resolving apparent contradictions in prior claims.

Findings

CTCs do not help distinguish nonorthogonal states in natural formulations

Nonlinear quantum mechanics does not improve solving hard computational problems

The output of CTC-assisted evolution on mixtures is not a convex combination of pure states outputs

Abstract

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.