Entanglement Islands from Hilbert Space Reduction
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 selfencoded, 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2022
 DOI:
 10.48550/arXiv.2211.17004
 arXiv:
 arXiv:2211.17004
 Bibcode:
 2022arXiv221117004B
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Quantum Physics
 EPrint:
 28pages. Comments are very welcome