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<p>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 <i>J</i><sub><i>W</i></sub>, quantum discord <i>D</i><sub><i>W</i></sub>, and one-shot distillable entanglement <i>E</i><sub><i>D</i></sub>, 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.</p>

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Zoo of correlation inequalities in holography and beyond

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月25日

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  • Kyan Louisia,
  • Takato Mori,
  • Herbie Warner

摘要

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 JW, quantum discord DW, and one-shot distillable entanglement ED, 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.