Proper and improper density matrices and the consistency of the Deutsch   model for Local Closed Timelike Curves
  We discuss the concept of proper and improper density matrixes and we argue that this issue is of fundamental importance for the understanding of the quantum-mechanical CTC model proposed by Deutsch. We arrive at the conclusion that under a realistic interpretation, the distinction between proper and improper density operators is not a relativistically covariant notion and this fact leads to the conclusion that the D-CTC model is physically inconsistent. 
A. C. Lobo, I. L. Paiva, P. R. Dieguez
quant-ph