Resource counting for conjugate-basis two-pass DAEPP

Determine the resource requirements of a DAHR variant using conjugate-basis two-pass DAEPP for general Werner channels, including whether the second pass requires a second robust auxiliary degree of freedom, such as frequency or time-bin, or an additional hyperentanglement pair.

Background

The paper analyzes a DAHR protocol that uses one spatial degree of freedom to purify polarization entanglement through a single DAEPP round. The authors identify a possible extension based on conjugate-basis two-pass DAEPP for general Werner channels, which could remove residual phase errors in addition to bit-flip errors.

The unresolved issue is the resource cost of this extension. A second purification pass may require either another robust auxiliary degree of freedom or a separate hyperentangled pair, and the paper does not determine which resources are necessary or how the alternatives compare.

References

Other open directions include DAHR variant which utilises conjugate-basis two-pass DAEPP for general Werner channels, which would clear the residual phase error on top of bit-flip error. The open question in that case would be resource counting, since the second pass would either require a second robust auxiliary DOF (e.g., frequency or time-bin as in ) or a second hyperentanglement pair altogether.

— Photon-efficient quantum repeater chains via hyperentanglement-assisted purification  (2608.30786 - Kumar et al., 31 Aug 2026) in Section 6, Summary and Outlook