Flat entanglement spectra in fixed-area states of quantum gravity

Understand

We use the Einstein-Hilbert gravitational path integral to investigate gravitational entanglement at leading order $O(1/G)$.

• We argue that semiclassical states prepared by a Euclidean path integral have the property that projecting them onto a subspace in which the Ryu-Takayanagi or Hubeny-Rangamani-Takayanagi surface has definite area gives a state with a flat entanglement spectrum at this order in gravitational perturbation theory.
• This means that the reduced density matrix can be approximated as proportional to the identity to the extent that its Renyi entropies $S_n$ are independent of $n$ at this order.
• The $n$-dependence of $S_n$ in more general states then arises from sums over the RT/HRT-area, which are generally dominated by different values of this area for each $n$.