Exact conservation for non-commuting charges

Determine how the state-transformation structure changes when non-commuting conserved charges must be conserved exactly, without allowing asymptotically vanishing violations, and characterize transformations within the resulting charge-entropy equivalence classes.

Background

The paper notes that prior methods for non-commuting charges rely crucially on allowing approximately charge-conserving unitaries. It leaves unresolved both the effect of imposing exact conservation and the appropriate characterization of transformations between states sharing the corresponding macroscopic quantities.

References

It remains unclear, however, how the transformation structure changes when the non-commuting charges have to be conserved exactly, i.e.~without allowing asymptotically vanishing charge-conservation violation, and how one should characterize transformations within the corresponding charge-entropy equivalence classes.

— From the Unknown to the Desired: Transforming Unknown Initial States in the Resource Theory of Work and Heat  (2609.09352 - Biswas et al., 8 Sep 2026) in Section Discussion and outlook, third paragraph