Zoo of Correlation Inequalities in Holography and Beyond

• URL: http://arxiv.org/abs/2511.21870v1
• Date: Wed, 26 Nov 2025 19:50:22 GMT
• Title: Zoo of Correlation Inequalities in Holography and Beyond
• Abstract summary: We study information-theoretic inequalities for holographic correlation measures $J_W$ and $D_W$.<n>We establish rigorous frameworks that prove monotonicity, monogamy, and strong superadditivity.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study information-theoretic inequalities for holographic correlation measures $J_W$ and $D_W$, establishing rigorous topological frameworks that prove monotonicity, monogamy, and strong superadditivity. While earlier work proposed bulk duals of classical correlation and quantum discord, their information-theoretic properties were unclear. We derive multiple inequalities involving entanglement wedge cross sections (EWCS) and show that monotonicity holds for both measured and unmeasured parties in $J_W$ and for the unmeasured party in $D_W$. Unlike their original counterparts, we find that $J_W$ is monogamous for both parties and obeys one-way strong superadditivity, whereas $D_W$ is polygamous for the unmeasured party in pure tripartite states. These results highlight distinctive features of holographic states and support a conjectured duality between $J_W$ and distillable entanglement. Motivated by the relation between EWCS and reflected entropy, we introduce boundary analogues $J_R$ and $D_R$, which serve as computable proxies for classical and quantum correlations without optimization. We analyze their inequalities, proving several and presenting counterexamples. Overall, we provide a systematic "zoo" of correlation inequalities in and beyond holography, clarifying connections among bulk geometry, discord-type correlations, and distillable entanglement.

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