Towards a complete classification of holographic entropy inequalities

• URL: http://arxiv.org/abs/2409.17317v1
• Date: Wed, 25 Sep 2024 19:55:31 GMT
• Title: Towards a complete classification of holographic entropy inequalities
• Authors: Ning Bao, Keiichiro Furuya, Joydeep Naskar,
• Abstract summary: We use a triality between holographic entropy inequalities, contraction maps and partial cubes. We show that the validity of a holographic entropy inequality is implied by the existence of a contraction map. We also demonstrate interesting by-products, most notably, a procedure to generate candidate quantum entropy inequalities.
• Score: 0.10923877073891444
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a deterministic method to find all holographic entropy inequalities and prove the completeness of our method. We use a triality between holographic entropy inequalities, contraction maps and partial cubes. More specifically, the validity of a holographic entropy inequality is implied by the existence of a contraction map, which we prove to be equivalent to finding an isometric embedding of a contracted graph. Thus, by virtue of the completeness of the contraction map proof method, the problem of finding all holographic entropy inequalities is equivalent to the problem of finding all contraction maps, which we translate to a problem of finding all image graph partial cubes. We give an algorithmic solution to this problem and characterize the complexity of our method. We also demonstrate interesting by-products, most notably, a procedure to generate candidate quantum entropy inequalities.

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