Question

Are black hole states completely mixed?

Answer 1

In Swingle's work Entanglement Renormalization and Holography, he mentioned that a black hole in AdS bulk corresponds to a finite temperature boundary state. With the MERA picture of the entanglement renormalization, the coarse grained state at the IR side becomes a completely mixed state.

I am not clear why the coarse grained state is a 'completely mixed state'. If the MERA structure is regarded as a unitary quantum operation (where the disentanglers are unitary and the isometries can also be regarded as unitary by adding ancilla |0⟩|0⟩ states). Then the coarse grained state of a thermal boundary state is a mixed state with a diagonal density matrix, but not necessarily a completely mixed state (unitary operation does not change the spectrum of the boundary state).