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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2309.02506 |
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| _version_ | 1866913239264133120 |
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| author | Couch, Josiah Nguyen, Phuc Racz, Sarah Stratis, Georgios Zhang, Yuxuan |
| author_facet | Couch, Josiah Nguyen, Phuc Racz, Sarah Stratis, Georgios Zhang, Yuxuan |
| contents | In recent work, Akers et al. proved that the entanglement of purification $E_p(A:B)$ is bounded below by half of the $q$-Rényi reflected entropy $S_R^{(q)}(A:B)$ for all $q\geq2$, showing that $E_p(A:B) = \frac{1}{2} S_R^{(q)}(A:B)$ for a class of random tensor network states. Naturally, the authors raise the question of whether a similar bound holds at $q = 1$. Our work answers that question in the negative by finding explicit counter-examples, which we arrive at through numerical optimization.
Nevertheless, this result does not preclude the possibility that restricted sets of states, such as CFT states with semi-classical gravity duals, could obey the bound in question. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02506 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | One-half reflected entropy is not a lower bound for entanglement of purification Couch, Josiah Nguyen, Phuc Racz, Sarah Stratis, Georgios Zhang, Yuxuan Quantum Physics High Energy Physics - Theory In recent work, Akers et al. proved that the entanglement of purification $E_p(A:B)$ is bounded below by half of the $q$-Rényi reflected entropy $S_R^{(q)}(A:B)$ for all $q\geq2$, showing that $E_p(A:B) = \frac{1}{2} S_R^{(q)}(A:B)$ for a class of random tensor network states. Naturally, the authors raise the question of whether a similar bound holds at $q = 1$. Our work answers that question in the negative by finding explicit counter-examples, which we arrive at through numerical optimization. Nevertheless, this result does not preclude the possibility that restricted sets of states, such as CFT states with semi-classical gravity duals, could obey the bound in question. |
| title | One-half reflected entropy is not a lower bound for entanglement of purification |
| topic | Quantum Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2309.02506 |