Which process matrices are physically realizable?
In plain words
The mathematics allows many exotic arrangements of operations, but only some can be built with real devices. The task is the exact list, for four or more parties and for processes that cannot be completed into a reversible one.
Precise statement
Wechs, Branciard and Oreshkov (2023) showed that every unitarily extendible tripartite process has a realization on time-delocalized subsystems. Determine (a) whether every unitarily extendible process with $N \ge 4$ parties has such a realization, and (b) whether processes with no unitary extension (no purification), such as the Oreshkov-Costa-Brukner bipartite process, admit any realization within standard quantum theory.
What would settle it
A realization theorem for unitarily extendible N-party processes, and a proof or counterexample for non-purifiable processes.
Status in the literature
Unverified note
Tripartite unitarily extendible processes are realizable on time-delocalized subsystems (2023); causally separable processes equal circuits with classical control of causal order (Wechs, Abbott, Branciard, arXiv:2609.20774; for the extensibly causally separable class also Wei and Pang, arXiv:2609.18559, September 2026); $N \ge 4$ and non-purifiable processes are open.