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arXiv:2602.12627 · Journal of High Energy Physics

Boundary mutual information in double holography

Yuxuan Liu, Yi Ling, Zhuo-Yu Xian

hep-thcond-mat.str-elgr-qcquant-phSubmitted Feb 13, 2026• Announced Feb 16, 2026• 0 citations
v1 · Feb 13, 2026v2 · Aug 5, 2026
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Abstract

We consider a composite system where AdS$_3$ gravity is coupled to a flat heat bath and investigate the mutual information between two subregions on the intersection of the AdS$_3$ and bath, referred to as the boundary mutual information (BMI). The corresponding entanglement entropy is captured via quantum extremal surfaces (QES), which holographically be computed by a surface optimization algorithm based on ``Surface Evolver''. We focus on both connected and disconnected configurations of the quantum entanglement wedge (Q-EW) in the AdS$_3$ bulk and analyze the finite corrections to the BMI. Our numerical results reveal a phase transition of the BMI as the separation between two subregions increases. Furthermore, we find that the BMI can naturally be decomposed into two distinct components: a geometric term arising from the areas of the quantum extremal surfaces, and a correction term resulting from bulk quantum fields within the Q-EW. Interestingly, the geometric contribution always exceeds the total BMI, indicating a negative correction from the bulk matter fields. This negativity can be understood as the result of subtracting a greater contribution from quantum fields in the connected Q-EW than in the disconnected one. We also reproduce the negative contribution of bulk quantum fields to BMI within a random tensor network (RTN) toy model of double holography. Modeling the bulk as a highly mixed state entangled with a large bath leads to a volume-law bulk entropy. In the large bond-dimension limit, the geometric part of the BMI remains non-negative, while the bulk entropy contribution becomes non-positive when the Q-EWs merge.

Journal reference
JHEP07(2026)110
DOI
10.1007/JHEP07(2026)110

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A bstract In the framework of double holography, we investigate the entanglement behavior of a subregion of the defect on the boundary of a CFT 3 . The entanglement entropy of this defect subregion is determined by the quantum extremal surface (QES) anchored at the two endpoints of the subregion from the brane perspective. We further analyze the entanglement entropy of the quantum matter within this QES, which can be extracted from the total entanglement entropy. We find there are two phases of the QES. To numerically distinguish these phases, we design a strategy for approaching the QES by progressively reducing the width of a semi-ellipse-like region within the CFT 3 , which is bounded by the defect. During this process, we discover an entanglement phase transition driven by the degree of freedom on the brane. In the shrinking phase, the entanglement wedge of the defect subregion sharply decreases to zero as the removal of the CFT 3 . In contrast, in the stable phase, the wedge almost remains constant. In this phase, the formulas of entanglement measures can be derived based on defect and CFT 3 central charges in the semi-classical limit. For entanglement entropy, the classical geometry only contributes a subleading term with logarithmic divergence, but the matter entanglement exhibits a dominant linear divergence, even in the semi-classical limit. For the reflected entropy within the defect subregion, classical geometry contributes a leading term with logarithmic divergence, while the quantum matter within the entanglement wedge only contributes a finite term.
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Abstract In the context of relating AdS/CFT to quantum information theory, we propose a holographic dual of Fisher information metric for mixed states in the boundary field theory. This amounts to a holographic measure for the distance between two mixed quantum states. For a spherical subregion in the boundary we show that this is related to a particularly regularized volume enclosed by the Ryu-Takayanagi surface. We further argue that the quantum correction to the proposed Fisher information metric is related to the quantum correction to the boundary entanglement entropy. We discuss consequences of this connection.
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Abstract Quantum states with geometric duals are known to satisfy a stricter set of entropy inequalities than those obeyed by general quantum systems. The set of allowed entropies derived using the Ryu-Takayanagi (RT) formula defines the Holographic Entropy Cone (HEC). These inequalities are no longer satisfied once general quantum corrections are included by employing the Quantum Extremal Surface (QES) prescription. Nevertheless, the structure of the QES formula allows for a controlled study of how quantum contributions from bulk entropies interplay with HEC inequalities. In this paper, we initiate an exploration of this problem by relating bulk entropy constraints to boundary entropy inequalities. In particular, we show that requiring the bulk entropies to satisfy the HEC implies that the boundary entropies also satisfy the HEC. Further, we also show that requiring the bulk entropies to obey monogamy of mutual information (MMI) implies the boundary entropies also obey MMI.
In the context of relating AdS/CFT to quantum information theory, we propose a holographic dual of Fisher information metric for mixed states in the boundary field theory. This amounts to a holographic measure for the distance between two mixed quantum states. For a spherical subregion in the boundary we show that this is related to a particularly regularized volume enclosed by the Ryu-Takayanagi surface. We further argue that the quantum correction to the proposed Fisher information metric is related to the quantum correction to the boundary entanglement entropy. We discuss consequences of this connection.