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arXiv · 2211.17004

Entanglement Islands from Hilbert Space Reduction

Debarshi Basu·Qiang Wen·Shangjie Zhou
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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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Debarshi Basu, Qiang Wen, Shangjie Zhou. 2022-11-30. Entanglement Islands from Hilbert Space Reduction. https://arxiv.org/abs/2211.17004

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