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Temporal Entanglement from Holographic Entanglement Entropy
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Temporal Entanglement from Holographic Entanglement Entropy
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Recently, several notions of entanglement in time have emerged as a novel frontier in quantum many-body physics, quantum field theory and gravity. We propose a systematic prescription to characterize temporal entanglement in relativistic quantum field theory in a general state for an arbitrary subregion on a flat, constant-time slice in a flat spacetime. Our prescriptions starts with the standard entanglement entropy of a spatial subregion and amounts to transporting the unchanged subregion to boosted time slices all the way across the light cone when it becomes in general a complex characterization of the corresponding temporal subregion. For holographic quantum field theories, our prescription amounts to an analytic continuation of all codimension-two bulk extremal surfaces satisfying the homology constraint and picking the one with the smallest real value of the area as the leading saddle point. We implement this prescription for holographic conformal field theories in thermal states on both a two-dimensional Lorentzian cylinder and three-dimensional Minkowski space, and show that it leads to results with self-consistent physical properties of temporal entanglement.
Forward citations
Cited by 12 Pith papers
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A bulk extremization prescription produces composite timelike-spacelike geodesics whose complex length exactly matches CFT two-point functions at timelike separation, including behind the BTZ horizon.
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For timelike boundary regions, the entanglement first law ΔS = Δ⟨H⟩ is equivalent, by the paper's proof, to the linearized Einstein equations around AdS.
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Timelike Holographic Complexity
Timelike subregion complexity within the holographic Complexity=Volume conjecture is computed for pure AdS and AdS black branes; it is purely real and shares the spacelike UV divergence structure.
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In asymptotically AdS black holes with space-like singularities, late-time linear growth of time-like entanglement entropy is governed by a critical extremal surface inside the event horizon, with growth rates bounded...
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