Adaptivity for entangled Gaussian measurements without conjugate states

Determine whether adaptivity is necessary for entangled Gaussian measurements to achieve energy‑independent sample complexity for single‑mode Gaussian state tomography when conjugate copies are not available.

Background

Non‑adaptive continuous‑variable Bell measurements on a state and its conjugate can achieve energy‑independent scaling, showing that certain resources can circumvent energy dependence.

However, in realistic scenarios where conjugate copies are unavailable, it is unknown whether adaptivity is required even when entangled Gaussian measurements across copies are allowed.

References

When conjugate states are not available, it remains unclear whether entangled Gaussian measurements need adaptivity to achieve energy independence.

— 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")