We propose a new duality relation between codimension-two space-like surfaces in gravitational theories and quantum states in dual Hilbert spaces. This surface| $/$ |state correspondence largely generalizes the idea of holography such that we do not need to rely on the existence of boundaries in gravitational spacetimes. The present idea is motivated by the recent interpretation of anti-de Sitter space| $/$ |conformal field theory (AdS| $/$ |CFT) in terms of the tensor networks, so-called MERA (multi-scale entanglement renormalization ansatz). Moreover, we study this correspondence from the viewpoint of entanglement entropy and an information metric. The Cramer–Rao bound in quantum estimation theory implies that the quantum fluctuations of the radial coordinate of the AdS are highly suppressed in the large-| $N$ | limit.We propose a new duality relation between codimension-two space-like surfaces in gravitational theories and quantum states in dual Hilbert spaces. This surface|$/$|state correspondence largely generalizes the idea of holography such that we do not need to rely on the existence of boundaries in gravitational spacetimes. The present idea is motivated by the recent interpretation of anti-de Sitter space|$/$|conformal field theory (AdS|$/$|CFT) in terms of the tensor networks, so-called MERA (multi-scale entanglement renormalization ansatz). Moreover, we study this correspondence from the viewpoint of entanglement entropy and an information metric. The Cramer–Rao bound in quantum estimation theory implies that the quantum fluctuations of the radial coordinate of the AdS are highly suppressed in the large-|$N$| limit.

arXiv:1503.03542Progress of Theoretical and Experimental PhysicsJul 1, 2015184 citations

Entanglement in Quantum Field Theory and Holography

Agon Quintero, César A. Alfonso

Jan 1, 20170 citations

Zoo of Correlation Inequalities in Holography and Beyond

Kyan Louisia, Takato Mori, Herbie Warner

Information-theoretic inequalities often impose nontrivial constraints on holographic states. In this work, we study measurement-based classical and quantum correlations in holography, focusing on the proposed duals of classical correlation $J_W$ , quantum discord $D_W$ , and one-shot distillable entanglement $E_D$ , defined in terms of the entanglement wedge cross section (EWCS). We develop a homological framework tailored to inequalities involving multiple EWCSs and Ryu-Takayanagi surfaces, and use it to prove a family of inequalities, including monotonicity and monogamy/polygamy-type relations, as well as one-way strong superadditivity. For strong superadditivity, we additionally confirm its two-way version using Haar random states. We also examine holography-inspired boundary duals in terms of the reflected entropy and provide proofs and counterexamples for their information-theoretic inequalities. Taken together, our results provide further evidence for the duality between the EWCS and its proposed boundary counterparts -- measurement-based correlations and one-shot distillable entanglement -- while also furnishing a unified, rigorous method for proving multi-EWCS inequalities.Information-theoretic inequalities often impose nontrivial constraints on holographic states. In this work, we study measurement-based classical and quantum correlations in holography, focusing on the proposed duals of classical correlation $J_W$, quantum discord $D_W$, and one-shot distillable entanglement $E_D$, defined in terms of the entanglement wedge cross section (EWCS). We develop a homological framework tailored to inequalities involving multiple EWCSs and Ryu-Takayanagi surfaces, and use it to prove a family of inequalities, including monotonicity and monogamy/polygamy-type relations, as well as one-way strong superadditivity. For strong superadditivity, we additionally confirm its two-way version using Haar random states. We also examine holography-inspired boundary duals in terms of the reflected entropy and provide proofs and counterexamples for their information-theoretic inequalities. Taken together, our results provide further evidence for the duality between the EWCS and its proposed boundary counterparts -- measurement-based correlations and one-shot distillable entanglement -- while also furnishing a unified, rigorous method for proving multi-EWCS inequalities.

hep-thCross-listedarXiv:2511.21870Nov 28, 20250 citations

Multipartite optimized correlation measures and holography

Oliver Dewolfe A, Joshua Levin, Graeme Smith

We explore ways to quantify multipartite correlations, in quantum information and in holography. We focus on optimized correlation measures, linear combinations of entropies minimized over all possible purifications of a state that satisfy monotonicity conditions. These contain far more information about correlations than entanglement entropy alone. We present a procedure to derive such quantities and construct a menagerie of symmetric optimized correlation measures on three parties. These include tripartite generalizations of the entanglement of purification, the squashed entanglement, and the recently introduced $Q$ correlation and $R$ correlation. Some correlation measures vanish only on product states and, thus, quantify both classical and quantum correlations; others vanish on any separable state, capturing quantum correlations alone. We then use a procedure motivated by the surface-state correspondence to construct holographic duals for the correlation measures as linear combinations of bulk surfaces. The geometry of the surfaces can preserve, partially break, or fully break the symmetry of the correlation measure. The optimal purification is encoded in the locations of certain points, whose locations are fixed by constraints on the areas of combinations of surfaces. This gives a new concrete connection between information theoretic quantities evaluated on a boundary state and detailed geometric properties of its dual.We explore ways to quantify multipartite correlations, in quantum information and in holography. We focus on optimized correlation measures, linear combinations of entropies minimized over all possible purifications of a state that satisfy monotonicity conditions. These contain far more information about correlations than entanglement entropy alone. We present a procedure to derive such quantities and construct a menagerie of symmetric optimized correlation measures on three parties. These include tripartite generalizations of the entanglement of purification, the squashed entanglement, and the recently introduced $Q$ correlation and $R$ correlation. Some correlation measures vanish only on product states and, thus, quantify both classical and quantum correlations; others vanish on any separable state, capturing quantum correlations alone. We then use a procedure motivated by the surface-state correspondence to construct holographic duals for the correlation measures as linear combinations of bulk surfaces. The geometry of the surfaces can preserve, partially break, or fully break the symmetry of the correlation measure. The optimal purification is encoded in the locations of certain points, whose locations are fixed by constraints on the areas of combinations of surfaces. This gives a new concrete connection between information theoretic quantities evaluated on a boundary state and detailed geometric properties of its dual.

arXiv:2007.11587Physical review. D/Physical review. D.Sep 8, 20207 citations

We propose a new duality relation between codimension-two space-like surfaces in gravitational theories and quantum states in dual Hilbert spaces. This surface|

/

|state correspondence largely generalizes the idea of holography such that we do not need to rely on the existence of boundaries in gravitational spacetimes. The present idea is motivated by the recent interpretation of anti-de Sitter space|

/

|conformal field theory (AdS|

/

|CFT) in terms of the tensor networks, so-called MERA (multi-scale entanglement renormalization ansatz). Moreover, we study this correspondence from the viewpoint of entanglement entropy and an information metric. The Cramer–Rao bound in quantum estimation theory implies that the quantum fluctuations of the radial coordinate of the AdS are highly suppressed in the large-|

N

| limit.

J_W

, quantum discord

D_W

, and one-shot distillable entanglement

E_D

, defined in terms of the entanglement wedge cross section (EWCS). We develop a homological framework tailored to inequalities involving multiple EWCSs and Ryu-Takayanagi surfaces, and use it to prove a family of inequalities, including monotonicity and monogamy/polygamy-type relations, as well as one-way strong superadditivity. For strong superadditivity, we additionally confirm its two-way version using Haar random states. We also examine holography-inspired boundary duals in terms of the reflected entropy and provide proofs and counterexamples for their information-theoretic inequalities. Taken together, our results provide further evidence for the duality between the EWCS and its proposed boundary counterparts -- measurement-based correlations and one-shot distillable entanglement -- while also furnishing a unified, rigorous method for proving multi-EWCS inequalities.

Q

correlation and

R

correlation. Some correlation measures vanish only on product states and, thus, quantify both classical and quantum correlations; others vanish on any separable state, capturing quantum correlations alone. We then use a procedure motivated by the surface-state correspondence to construct holographic duals for the correlation measures as linear combinations of bulk surfaces. The geometry of the surfaces can preserve, partially break, or fully break the symmetry of the correlation measure. The optimal purification is encoded in the locations of certain points, whose locations are fixed by constraints on the areas of combinations of surfaces. This gives a new concrete connection between information theoretic quantities evaluated on a boundary state and detailed geometric properties of its dual.