Island phase as a property of quantum state and Hilbert space

In this talk I will give a purely quantum information perspective for the Island formula. More explicitly we show that, in a quantum system when the state of a subset is totally encoded in the state of another subset, the Hilbert space of the system will reduce, and the way we compute the reduced density matrix and related entropy quantities will also change essentially. Such reductions of the Hilbert space result in a new island formula in quantum systems, which we conjecture to be the same island formula in gravity recently proposed to rescue the unitarity for black hole evaporation. Furthermore, we propose a non-gravitational field theory configuration where entanglement islands emerge, give a description for the entanglement structure of the island phase and propose how to realize the island phase in the lab.