Develop an experimentally accessible readout for spin GKP states

Develop a practical measurement protocol that accesses the phase information stored in spin GKP states using experimentally available collective operations and measurements.

Background

The numerical optimization identifies spin GKP states as the globally optimal or near-optimal probes within the permutationally symmetric sector for sufficiently large ensembles. These states have a localized grid structure on the Bloch sphere and are related to bosonic GKP states, whose error-correction procedures involve recovery maps and syndrome measurements.

The paper emphasizes that, unlike for spin grid states, it does not provide a practical method for extracting the phase information encoded in spin GKP states. This leaves unresolved how the metrological potential of the globally optimal probes could be realized experimentally.

References

Likewise, for spin GKP states it is unclear how to access the phase information stored in these states.

— Spin Grid States for Quantum Metrology in Atomic Clocks Limited by Spontaneous Emission  (2609.16975 - Burgath et al., 15 Sep 2026) in Section “Conclusion and Outlook”

Furthermore, bosonic GKP states can be prepared by collective emission of spin GKP states [ A natural question is whether a similar mapping of SGSs to the bosonic phase space still resembles a grid pattern.

— Spin Grid States for Quantum Metrology in Atomic Clocks Limited by Spontaneous Emission  (2609.16975 - Burgath et al., 15 Sep 2026) in Section “Conclusion and Outlook”