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The Quantum Null Energy Condition, Entanglement Wedge Nesting, and Quantum Focusing
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abstract
We study the consequences of Entanglement Wedge Nesting for CFTs with holographic duals. The CFT is formulated on an arbitrary curved background, and we include the effects of curvature-squared couplings in the bulk. In this setup we find necessary and sufficient conditions for Entanglement Wedge Nesting to imply the Quantum Null Energy Condition in $d\leq 5$, extending its earlier holographic proofs. We also show that the Quantum Focusing Conjecture yields the Quantum Null Energy Condition as its nongravitational limit under these same conditions.
Forward citations
Cited by 3 Pith papers
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Combinatorial aspects of holographic quantum secret sharing
Bulk regions in AdS3/CFT2 get a holographic secret-sharing distance d and thresholds (r,s), with r = n - d + 1; pure states satisfy s = d - 1 while mixed states can satisfy s >= d.
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Tests of restricted Quantum Focusing and a new CFT bound
From rQFC, a new CFT bound follows that forbids the QNEC from saturating faster than O(Σ^{d−2}) in near-vacuum states, while rQFC is proven in JT gravity and explicit QFC counterexamples are constructed.
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Constraints from Entanglement Wedge Nesting for Holography at a Finite Cutoff
For holography with a finite ETW-brane cutoff, entanglement wedge nesting requires the two intervals' RT surfaces to be spacelike separated, a condition stronger than spacelike separation of the intervals themselves.
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