Curator's Take
This article settles a long‑standing question by proving that both bosonic and fermionic Gaussian states can be reconstructed with only O(n²) copies, where n is the number of modes, regardless of purity or energy constraints. The result bridges a gap between theoretical guarantees for generic quantum state tomography and the practical needs of photonic, superconducting, and cold‑atom platforms that routinely work with Gaussian resources. By leveraging representation theory of Gaussian unitaries, the authors provide a scalable pathway for rapid verification and benchmarking of near‑term quantum devices that rely on these states.
— Mark Eatherly
Summary
The sample complexity is the minimum number of copies required to learn an accurate classical description of a quantum state. Bosonic and fermionic Gaussian quantum states are families of quantum states that play a key role in quantum science and technology, from quantum optics and many-body physics to quantum chemistry, quantum computing, and quantum information theory. Despite their importance, their sample complexity had not been fully determined. We settle this open problem and show that both bosonic and fermionic Gaussian states can be learned using a number of copies that scales quadratically in the number of modes, regardless of whether the state is pure or mixed, and independently of any energy bound on the state. We derive these results by using the representation theory of Gaussian unitaries and by putting forth a generalization of the random purification channel to this setting and beyond.