Probing phase transitions of holographic entanglement entropy with fixed area states

103

We show that a naïve application of the quantum extremal surface (QES) prescription can lead to paradoxical results and must be corrected at leading order. The corrections arise when there is a second QES (with strictly larger generalized entropy at leading order than the minimal QES), together with a large amount of highly incompressible bulk entropy between the two surfaces. We trace the source of the corrections to a failure of the assumptions used in the replica trick derivation of the QES prescription, and show that a more careful derivation correctly computes the corrections. Using tools from one-shot quantum Shannon theory (smooth min- and max-entropies), we generalize these results to a set of refined conditions that determine whether the QES prescription holds. We find similar refinements to the conditions needed for entanglement wedge reconstruction (EWR), and show how EWR can be reinterpreted as the task of one-shot quantum state merging (using zero-bits rather than classical bits), a task gravity is able to achieve optimally efficiently.

Section: Jhep04(2021)062mentioning

confidence: 91%

Section: Jhep04(2021)062mentioning

confidence: 97%

Section: Overview Of Papermentioning

confidence: 99%

Section: Jhep04(2021)062mentioning

confidence: 99%

See 2 more Smart Citations

Leading order corrections to the quantum extremal surface prescription

Akers

Penington

2021

103

“…Below the minimal size, the relative entropy is zero, while above that size, the relative entropy becomes finite and grows with the size. At finite S 0 , we expect to have a smooth curve instead of a sharp transition, see [50][51][52].…”

Section: Jhep03(2021)040mentioning

confidence: 99%

Signatures of global symmetry violation in relative entropies and replica wormholes

Chen

Lin

2021

It is widely believed that exact global symmetries do not exist in theories that admit quantum black holes. Here we propose a way to quantify the degree of global symmetry violation in the Hawking radiation of a black hole by using certain relative entropies. While the violations of global symmetry that we consider are non-perturbative effects, they nevertheless give $$ \mathcal{O} $$ O (1) contributions to the relative entropy after the Page time. Furthermore, using “island” formulas, these relative entropies can be computed within semi-classical gravity, which we demonstrate with explicit examples. These formulas give a rather precise operational sense to the statement that a global charge thrown into an old black hole will be lost after a scrambling time.The relative entropies considered here may also be computed using a replica trick. At integer replica index, the global symmetry violating effects manifest themselves as charge flowing through the replica wormhole.

Reflected entropy in random tensor networks. Part II. A topological index from canonical purification

Akers

Faulkner

Lin

et al. 2023

In ref. [1], we analyzed the reflected entropy (SR) in random tensor networks motivated by its proposed duality to the entanglement wedge cross section (EW) in holographic theories, $$ {S}_R=2\frac{EW}{4G} $$ S R = 2 EW 4 G . In this paper, we discover further details of this duality by analyzing a simple network consisting of a chain of two random tensors. This setup models a multiboundary wormhole. We show that the reflected entanglement spectrum is controlled by representation theory of the Temperley-Lieb algebra. In the semiclassical limit motivated by holography, the spectrum takes the form of a sum over superselection sectors associated to different irreducible representations of the Temperley-Lieb algebra and labelled by a topological index k ∈ ℤ>0. Each sector contributes to the reflected entropy an amount $$ 2k\frac{EW}{4G} $$ 2 k EW 4 G weighted by its probability. We provide a gravitational interpretation in terms of fixed-area, higher-genus multiboundary wormholes with genus 2k – 1 initial value slices. These wormholes appear in the gravitational description of the canonical purification. We confirm the reflected entropy holographic duality away from phase transitions. We also find important non-perturbative contributions from the novel geometries with k ≥ 2 near phase transitions, resolving the discontinuous transition in SR. Along with analytic arguments, we provide numerical evidence for our results. We finally speculate that signatures of a non-trivial von Neumann algebra, connected to the Temperley-Lieb algebra, will emerge from a modular flowed version of reflected entropy.