LOCC implementation of capacity-achieving protocols for noisy Gaussian channels

Determine whether the PPT-assisted capacity-achieving protocols for noisy thermal-loss, thermal-amplifier, and additive Gaussian-noise channels can be implemented using LOCC without sacrificing the communication rate or the imposed input-energy budget.

Background

The paper establishes exact quantum communication and entanglement-distribution capacities for three bosonic Gaussian channel families when assistance is allowed from completely PPT-preserving operations. Because LOCC is a strict subclass of these operations, the results do not determine the corresponding ordinary LOCC capacities for noisy channels.

The paper shows that the particular threshold maps used in its constructions are non-separable, but explicitly notes that this does not rule out different LOCC constructions achieving the same rates. Resolving whether such a rate-preserving LOCC reduction exists would also determine the ordinary secret-key capacity in the unconstrained setting through the stated capacity relations.

References

Whether the reduction exists for noisy channels remains an open question in quantum information theory.

— PPT-assisted capacities of bosonic Gaussian channels  (2610.26783 - Barber et al., 19 Oct 2026) in Section 4, Conclusions

Intermediate thresholds, finite-error refinements and optimal noisy-channel LOCC rates remain open.

— PPT-assisted capacities of bosonic Gaussian channels  (2610.26783 - Barber et al., 19 Oct 2026) in Appendix, Section 9, subsection “A sharper finite-block equality”