Entanglement Islands from Hilbert space reduction

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 exist 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 \(\hbox {CFT}_2\) with a special Weyl transformation.