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Minimal Purifications, Wormhole Geometries, and the Complexity=Action Proposal

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arxiv 1811.03113 v2 pith:3KJXRICJ submitted 2018-11-07 hep-th quant-ph

Minimal Purifications, Wormhole Geometries, and the Complexity=Action Proposal

classification hep-th quant-ph
keywords entanglementactioncomplexityminimalpurificationstatesboundarycorrespondence
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We define a new criterion for selecting a specific minimal entanglement purification of given mixed states in generic quantum states using the entanglement of purification. We then propose that its holographic dual is the state living on the boundary of the entanglement wedge in the surface-state correspondence. Finally, we make some remarks about the relationship between this and the complexity equals action proposals.

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    A cross-ratio threshold relation η'/η = e^{ΔH/2} governs entanglement-wedge phase transitions on pure-state holographic geometries, and uberholography's fractal dimension α ≈ 0.786 persists on asymptotic boundaries bu...