The D-CTC condition is generically fulfilled in classical (non-quantum) statistical systems

TL;DR

This paper demonstrates that the D-CTC condition, originally formulated for quantum systems with closed timelike curves, can also be generically satisfied in classical statistical systems, indicating it is not exclusive to quantum mechanics.

Contribution

The study extends Deutsch's proof for quantum systems to classical statistical systems, showing the D-CTC condition is broadly applicable beyond quantum contexts.

Findings

D-CTC condition can be fulfilled in classical systems under general conditions

Convexity and completeness of state space are key to the proof

D-CTC condition is not inherently quantum

Abstract

The D-CTC condition, introduced by David Deutsch as a condition to be fulfilled by analogues for processes of quantum systems in the presence of closed timelike curves, is investigated for classical statistical (non-quantum) bi-partite systems. It is shown that the D-CTC condition can generically be fulfilled in classical statistical systems, under very general, model-independent conditions. The central property used is the convexity and completeness of the state space that allows it to generalize Deutsch's original proof for q-bit systems to more general classes of statistically described systems. The results demonstrate that the D-CTC condition, or the conditions under which it can be fulfilled, is not characteristic of, or dependent on, the quantum nature of a bi-partite system.