Purification of Mixed State with Closed Timelike Curve is not Possible

TL;DR

This paper proves that unlike ordinary quantum states, mixed states passing through closed timelike curves cannot be universally purified, indicating the existence of proper and improper mixtures in such scenarios.

Contribution

It demonstrates the impossibility of purifying mixed states involving closed timelike curves within a consistent quantum framework.

Findings

Purification of CTC mixed states is impossible.

Existence of proper and improper mixtures in CTC quantum theory.

No universal Hilbert space purification for CTC states.

Abstract

In ordinary quantum theory any mixed state can be purified in an enlarged Hilbert space by bringing an ancillary system. The purified state does not depend on the state of any extraneous system with which the mixed state is going to interact and on the physical interaction. Here, we prove that it is not possible to purify a mixed state that traverses a closed time like curve (CTC) and allowed to interact in a consistent way with a causality-respecting (CR) quantum system in the same manner. Thus, in general for arbitrary interactions between CR and CTC systems there is no universal 'Church of the larger Hilbert space' for mixed states with CTC. This shows that in quantum theory with CTCs there can exist 'proper' and 'improper' mixtures.