Quantum computation with indefinite causal structures

Understand

One way to study the physical plausibility of closed timelike curves (CTCs) is to examine their computational power.

• This has been done for Deutschian CTCs (D-CTCs) and post-selection CTCs (P-CTCs), with the result that they allow for the efficient solution of problems in PSPACE and PP, respectively.
• Since these are extremely powerful complexity classes, which are not expected to be solvable in reality, this can be taken as evidence that these models for CTCs are pathological.
• This problem is closely related to the nonlinearity of this models, which also allows for example cloning quantum states, in the case of D-CTCs, or distinguishing non-orthogonal quantum states, in the case of P-CTCs.