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Entropy Inequalities Constrain Holographic Erasure Correction.
Bartłomiej Czech1, Sirui Shuai1, Yixu Wang1
1Tsinghua University, Institute for Advanced Study, Beijing 100084, China.
Physical Review Letters
|October 19, 2025
Summary
Holographic entropy inequalities are interpreted as erasure correction codes. Non-saturating inequalities are necessary for holographic erasure correction, shown by overlapping entanglement wedges in the bulk.
Area of Science:
- Quantum information theory
- Holographic principle
- Black hole thermodynamics
Background:
- The holographic principle suggests a connection between gravity in higher dimensions and quantum field theory in lower dimensions.
- Entropy inequalities in quantum information theory provide fundamental bounds on information processing.
- Black hole thermodynamics relates gravitational properties to thermodynamic quantities, including entropy.
Purpose of the Study:
- To interpret holographic entropy inequalities within the framework of erasure correction codes.
- To establish a connection between the saturation of these inequalities and the feasibility of holographic erasure correction schemes.
- To explore the geometric manifestations of these concepts in the bulk spacetime.
Main Methods:
- Utilizing concepts from quantum information theory, specifically focusing on entropy inequalities.
- Applying the holographic principle to translate properties between boundary and bulk theories.
- Analyzing the structure of entanglement wedges and their overlaps in the bulk spacetime.
Main Results:
- Holographic entropy inequalities can be understood as constraints on holographic erasure correction.
- The nonsaturation of an inequality is identified as a necessary condition for successful holographic erasure correction.
- Nonempty overlaps of entanglement wedges in the bulk are shown to be the physical manifestation of this condition.
Conclusions:
- The study provides a novel interpretation of holographic entropy inequalities through the lens of erasure correction.
- This work establishes a concrete link between abstract inequalities and physical properties in holographic duality.
- The findings offer new insights into the interplay between quantum information, gravity, and spacetime geometry.
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