Entanglement Islands from Hilbert Space Reduction
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866918017775960064 |
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| author | Basu, Debarshi Wen, Qiang Zhou, Shangjie |
| author_facet | Basu, Debarshi Wen, Qiang Zhou, Shangjie |
| contents | In this paper we propose a mechanism to generate entanglement islands in quantum systems from a purely quantum information perspective. More explicitly we show that, if we impose certain constraints on a quantum system by projecting out certain states in the Hilbert space, it is possible that for all the states remaining in the reduced Hilbert space, there exits subsets $I_a$ whose states are encoded in the states of another subset $\mathcal{R}_a$. Then the subsets $\{I_a\}$ are just the entanglement islands of the corresponding subsets $\{\mathcal{R}_a\}$. We call such a system self-encoded, and find that the entanglement entropy in such systems should be calculated by a new island formula. We give a comparison between our new island formula and island formula in gravitational theories. Inspired by our mechanism, we propose a simulation of the AdS/BCFT correspondence and the island phases in this context via a holographic CFT$_2$ with a special Weyl transformation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_17004 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Entanglement Islands from Hilbert Space Reduction Basu, Debarshi Wen, Qiang Zhou, Shangjie High Energy Physics - Theory General Relativity and Quantum Cosmology Quantum Physics In this paper we propose a mechanism to generate entanglement islands in quantum systems from a purely quantum information perspective. More explicitly we show that, if we impose certain constraints on a quantum system by projecting out certain states in the Hilbert space, it is possible that for all the states remaining in the reduced Hilbert space, there exits subsets $I_a$ whose states are encoded in the states of another subset $\mathcal{R}_a$. Then the subsets $\{I_a\}$ are just the entanglement islands of the corresponding subsets $\{\mathcal{R}_a\}$. We call such a system self-encoded, and find that the entanglement entropy in such systems should be calculated by a new island formula. We give a comparison between our new island formula and island formula in gravitational theories. Inspired by our mechanism, we propose a simulation of the AdS/BCFT correspondence and the island phases in this context via a holographic CFT$_2$ with a special Weyl transformation. |
| title | Entanglement Islands from Hilbert Space Reduction |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Quantum Physics |
| url | https://arxiv.org/abs/2211.17004 |