Proper and improper density matrices and the consistency of the Deutsch model for Local Closed Timelike Curves

TL;DR

This paper examines the distinction between proper and improper density matrices in quantum mechanics, arguing that Deutsch's CTC model is physically inconsistent due to non-covariance of this distinction.

Contribution

It clarifies the fundamental issues of proper and improper density matrices in the context of Deutsch's CTC model and demonstrates its physical inconsistency.

Findings

Proper and improper density matrices are not relativistically covariant

Deutsch's CTC model is inconsistent under realistic interpretations

The distinction impacts the physical validity of quantum CTC models

Abstract

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.