Robust signatures of collective non-Gaussianity

Determine whether collective non-Gaussianity that cannot be removed by local operations provides robust signatures of quantum phases, critical phenomena, or many-body dynamics, beyond the exponential Gaussian rank arising from independently accumulated local resources.

Background

The paper proves exponential Gaussian-rank growth for tensor powers even when the resource is supplied independently across copies. It therefore distinguishes, as a prospective research direction, the accumulation of independent local resources from collective non-Gaussianity that persists under local operations. Whether the latter has robust physical signatures in phases, critical phenomena, or many-body dynamics is explicitly left unresolved.

References

Finally, tensor powers exhibit exponential Gaussian rank without correlations between copies, this motivates distinguishing the accumulation of independent local resources from collective non-Gaussianity that cannot be removed by local operations, and investigating whether the latter provides robust signatures of quantum phases, critical phenomena, or many-body dynamics.

— Robust exponential lower bounds for fermionic and bosonic Gaussian ranks  (2610.02172 - Wei et al., 1 Oct 2026) in Section Discussion and outlook