Independently smoothed one-shot merging costs

Determine whether one-shot multiparty state-merging costs admit an independently smoothed formulation as conjectured by Dutil and Hayden.

Background

The paper distinguishes the simultaneous quantum typicality and one-shot min-entropy-smoothing conjectures that it disproves from other operational conjectures concerning multiparty state merging. In particular, it notes that Dutil and Hayden proposed an independently smoothed formulation of one-shot merging costs, but the paper does not analyze or resolve that conjecture.

Because this conjecture concerns a separate operational formulation rather than the simultaneous typicality statements refuted in the paper, it remains an unresolved question within the scope of the paper.

References

For example, Dutil's direct multiparty merging analysis beyond two senders uses the typicality conjecture Sec.~3.2.4, while Dutil and Hayden conjecture independently smoothed one-shot merging costs Conjecture~12.

— The Failure of Simultaneous Quantum Typicality  (2609.25726 - Collins, 22 Sep 2026) in Introduction, historical developments paragraph (discussion of related operational conjectures)