Existence of processes violating causal inequalities on time-delocalised subsystems.

Abstract in brief

• The paper discusses how certain quantum and classical processes can exist without a clear causal order, meaning operations may not follow a traditional "cause-and-effect" sequence, and explores whether these processes can be practically implemented.
• It introduces the concept of "timedelocalised quantum subsystems" as a framework to realize such processes within standard quantum theory, demonstrating that all unitary extensions of tripartite processes can be realized this way, including those that violate causal inequalities.
• The authors analyze a specific classical process with a unitary extension, showing it can be implemented on timedelocalised subsystems, and argue that these findings support the idea that causal inequalities are relevant for understanding when a definite causal order is absent in quantum and classical systems.]