Entangled Gaussian measurements and energy-dependent lower bounds

Determine whether the linear‑in‑energy sample‑complexity lower bound for non‑adaptive single‑copy Gaussian measurements in single‑mode Gaussian state tomography also holds for non‑adaptive entangled (multi‑copy) Gaussian measurements.

Background

The paper proves that any non‑adaptive, non‑entangling (single‑copy) Gaussian measurement scheme for single‑mode states must use Omega(E/ε^2) samples, establishing the necessity of adaptivity for energy‑independent scaling in that setting.

It remains unresolved whether allowing entangled, multi‑copy Gaussian measurements (still non‑adaptive) can overcome this lower bound.