Hidden quantum-informatic symmetries of quasi-de Sitter backgrounds

We investigate how degeneracies in quasi-de Sitter backgrounds, in the sense of Wands' duality, are reflected in real-space quantum correlations of primordial perturbations. Using the continuous-variable Gaussian formalism for coarse-grained scalar fluctuations, we construct the covariance matrix of a pair of spatially localized modes in inflationary spacetime, and extract the symplectic invariants of the system. For a generic Wands-dual pair of backgrounds, we find that while the individual entries of the covariance matrix are highly background-dependent, the symplectic eigenvalues -- and hence the entanglement entropy, mutual information, quantum discord and log-negativity -- all coincide for the two dual realizations. Our results unveil a new ''quantum-informatic symmetry'' of the de Sitter vacuum, according to which local linear entanglement witnesses constructed from coarse-grained fields cannot distinguish between Wands-dual inflationary histories, even though their background trajectories differ. We show that the special nature of the Wands-duality symmetry (of being local, scale-independent canonical transformations) is at the heart of this duality.