Measurement complexity of non-Gaussian noise spectroscopy

Determine the measurement complexity of estimating selected higher-order correlations or polyspectral coefficients in non-Gaussian noise spectroscopy under constraints on pulse bandwidth, sensor coherence, and quantum memory.

Background

The paper presents Quantum Phase-Space Inference (QΨ) as a framework for comparing sensing architectures and learning objectives under explicit operational constraints. The authors identify non-Gaussian noise spectroscopy as an application in which higher-order correlations and polyspectral coefficients must be estimated rather than merely local parameters.

The unresolved problem is to characterize the measurement complexity of these observables while accounting simultaneously for experimentally relevant restrictions on pulse bandwidth, sensor coherence time, and available quantum memory. Such a characterization would clarify whether quantum control or memory can provide provable advantages for higher-order noise characterization.

References

Several open problems in quantum sensing of classical fields admit natural formulations within our framework. In non-Gaussian noise spectroscopy, one may ask for the measurement complexity of estimating a selected higher-order correlation or polyspectral coefficient under constraints on pulse bandwidth, sensor coherence, and quantum memory [56, 57, 58].

— Exponential quantum advantage for learning signals with a single qubit  (2608.13521 - Kannan et al., 13 Aug 2026) in Appendix A.2, section “Quantum sensing”