Characterize convertibility under T-symmetric superchannels

Determine necessary and sufficient criteria for converting one kinematic T-violation resource into another by a T-symmetric superchannel, including the special case of conversions between unitary channels.

Background

The paper develops resource monotones and proves several explicit conversion results, including the existence of a universal quantum golden unit and a classical golden unit. These monotones provide necessary conditions for convertibility, but they do not completely determine the conversion preorder.

The unresolved issue is to obtain criteria that are both necessary and sufficient, even when the admissible resources are restricted to pure resources represented by unitary channels. The paper identifies a complete characterization of convertibility for kinematic T-violation as an important direction for future work.

References

We do not, however, obtain necessary and sufficient criteria for convertibility, even after restricting to pure resources, i.e., unitary channels. Such criteria are known in particular resource theories, including entanglement, coherence, and imaginarity. A complete characterization of convertibility for T-violation remains an important direction for future work.

— Dynamical resource theory of time-reversal symmetry breaking  (2609.36408 - Miyazaki et al., 29 Sep 2026) in Section 4.3, subsection “Convertibility and golden units”