Zoo of Correlation Inequalities in Holography and Beyond
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| Format: | Preprint |
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2025
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| author | Louisia, Kyan Mori, Takato Warner, Herbie |
| author_facet | Louisia, Kyan Mori, Takato Warner, Herbie |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_21870 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Zoo of Correlation Inequalities in Holography and Beyond Louisia, Kyan Mori, Takato Warner, Herbie High Energy Physics - Theory Quantum Physics 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. |
| title | Zoo of Correlation Inequalities in Holography and Beyond |
| topic | High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2511.21870 |