Entanglement Islands from Hilbert Space Reduction

• URL: http://arxiv.org/abs/2211.17004v5
• Date: Tue, 2 Apr 2024 14:25:55 GMT
• Title: Entanglement Islands from Hilbert Space Reduction
• Authors: Debarshi Basu, Qiang Wen, Shangjie Zhou,
• Abstract summary: We show that for all the states remaining in the Hilbert space, there exits subsets $I_a$ whose states are encoded in the states of another subset $mathcalR_a$. We call such a system self-encoded, and find that the entanglement entropy in such systems should be calculated by a new island formula.
• Score: 5.087405608698016
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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