Towards a complete classification of holographic entropy inequalities
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909538097037312 |
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| author | Bao, Ning Furuya, Keiichiro Naskar, Joydeep |
| author_facet | Bao, Ning Furuya, Keiichiro Naskar, Joydeep |
| contents | We propose a deterministic method to find all holographic entropy inequalities that have corresponding contraction maps and argue 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 argued 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17317 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards a complete classification of holographic entropy inequalities Bao, Ning Furuya, Keiichiro Naskar, Joydeep High Energy Physics - Theory Discrete Mathematics Quantum Physics We propose a deterministic method to find all holographic entropy inequalities that have corresponding contraction maps and argue 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 argued 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. |
| title | Towards a complete classification of holographic entropy inequalities |
| topic | High Energy Physics - Theory Discrete Mathematics Quantum Physics |
| url | https://arxiv.org/abs/2409.17317 |