Learning (tomography of) non‑unitary Gaussian channels

Develop upper and lower bounds on the query complexity of learning general (non‑unitary) bosonic Gaussian channels, extending beyond the current results for Gaussian unitary channels.

Background

While the paper focuses on state tomography, it points to Gaussian process (channel) tomography as a natural and important extension with practical relevance (e.g., sensing models).

At present, only Gaussian unitary channels have established upper bounds; the non‑unitary case lacks both upper and lower bounds, leaving the basic efficiency limits unresolved.

References

Another important direction for future work concerns tomography of Gaussian processes. Can our techniques be extended to establish lower and upper bounds on the query complexity of learning Gaussian channels? At present, upper bounds are known only in the restricted setting of Gaussian unitary channels, while the general case of non-unitary Gaussian channels remains open and lower bounds are entirely unexplored.

— Towards sample-optimal learning of bosonic Gaussian quantum states  (2603.18136 - Chen et al., 18 Mar 2026) in Open problems, Section 5.2 ("Open problems")