Abstract
We discuss two methods that, through a combination of cyclically gluing copies of a given n-party boundary state in AdS/CFT and a canonical purification, creates a bulk geometry that contains a boundary homologous minimal surface with area equal to 2 or 4 times the n-party entanglement wedge cross-section, depending on the parity of the party number and choice of method. The areas of the minimal surfaces are each dual to entanglement entropies that we define to be candidates for the n-party reflected entropy. In the context of AdS3/CFT2, we provide a boundary interpretation of our construction as a multiboundary wormhole, and conjecture that this interpretation generalizes to higher dimensions.
Highlights
One recent example in this direction is the conjecture that the entanglement of purification EP [3] is computed by the area of a particular bulk minimal surface called the entanglement wedge cross-section EW [4, 5]
In the context of AdS3/CFT2, we provide a boundary interpretation of our construction as a multiboundary wormhole, and conjecture that this interpretation generalizes to higher dimensions
We argue that the boundary interpretation of these bulk geometries, at least in three dimensions, is as a multiboundary wormhole with low-party number entanglement of the kind described in [30]
Summary
We first briefly review the construction of the n-party entanglement wedge cross-section in [6]. Divide the boundary into n new regions {A1, . Σi is homologous to Ai inside the entanglement wedge of the full boundary system A1 ∪ . ∪ An. The entanglement wedge cross-section is defined as the area in Planck units of ΣA1...An, minimized over all choices of {A1, . This quantity is conjectured to compute the multipartite entanglement of purification of the boundary subregions [6, 10]: n. Where the minimization is over all purifications |ψ A1A1...AnAn of the original state ρA1...An. We note that definition of the multipartite EW in [6] reduces to twice the entanglement wedge cross-section defined in [4].
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