Efficient construction of all-horizon closed devices

Identify which fixed finite-dimensional quantum channels admit efficient all-horizon closed-device implementations, with explicit bounds on circuit size or latency, for the adaptive complete-service model studied in the paper.

Background

Theorem~\ref{thm:causal-balancing} proves existence of an all-horizon closed device from a suitable finite exact collision, but the witness is selected existentially rather than constructed algorithmically. The theorem also makes no claim about circuit complexity or latency.

The conclusion therefore leaves unresolved the classification of channels for which efficient implementations are possible. The dephasing example supplies one explicit efficient corner, but the paper does not determine whether comparable efficient constructions exist for other channels.

References

Efficiency: the all-horizon device of Theorem~\ref{thm:causal-balancing} is built from a witness that is not constructed, and no circuit-size or latency claim is made; the streaming realization for dephasing shows that some corners admit explicit efficient devices, and which channels do is open.

— Bath dimension and initial entropy for closed repeated use of a quantum channel  (2609.18267 - Douglas, 16 Sep 2026) in Section 6, “Conclusion and open questions” (\label{sec:conclusion})