  We examine mixedness and entanglement of the chronology-respecting (CR)
system with assuming that quantum mechanical closed timelike curves (CTCs)
exist in nature and by introducing the qubit system and applying the general
controlled operations between CR and CTC systems. We use the magnitude of Bloch
vector as a measure of mixedness. While Deutschian-CTC (D-CTC) either preserves
or decreases the magnitude, postselected-CTC (P-CTC) can increases it.
Nonintuitively, even the completely mixed CR-qubit can be converted into a pure
state after CTC-qubit travels around the P-CTC. It is also shown that while
D-CTC cannot increase the entanglement of CR system, P-CTC can increase it.
Surprisingly, any partially entangled state can be maximally entangled pure
state if P-CTC exists. Thus, distillation of P-CTC-assisted entanglement can be
easily achieved without preparing the multiple copies of the partially
entangled state.
