Black hole merger as an event converting two qubits into one

A black hole represents a quantum state that saturates three bounds of the quantum orthogonalization interval. It is a qubit in an equal superposition of its two energy eigenstates, with a vanishing ground state and a nonvanishing one equal to the black hole’s energy, where the product of the black hole’s entropy and temperature amounts to half of its energy. As two black holes frequently merge into one, it is natural to ask what happens with the qubits they carry. I consider a binary black hole as a quantum system of two independent qubits evolving independently under a common Hamiltonian to show that their merger can be considered in terms of two orthogonal projections of this Hamiltonian onto a two-dimensional Hilbert subspace, which correspond to the Bell states of this two-qubit system.