A black hole represents a quantum state that saturates three bounds for the quantum orthogonalization interval. It is a qubit in an equal superposition of its two energy eigenstates, with a vanishing ground state and the nonvanishing one equal to the black hole energy, where the product of the black hole's entropy and temperature amounts to half of the black hole's energy. As two black holes frequently merge into one, it is natural to ask what happens with the qubits they carry. We 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 that also correspond to the Bell states of this two-qubit system.