A Stringy Universe
Meanwhile, I have been looking again at certain stringy black holes in four dimensions whose entropy is measured by quantities that occur very naturally in the study of entanglement. One may well ask where the $d = 4$ comes from in the quantum information theory, because obviously the messy string theory derivation is quite unimportant compared to these more fundamental considerations.
Well, notice that the three spatial dimensions from $d=4$ matches the number of MUBs for a qubit. Similarly, $d=5$ black holes mysteriously require qutrit states, which have four basic MUBs. Moreover, if one correctly accounts for the fourth roots in the Pauli MUB case, one might guess the dimension should be 6, which happens to be the dimension of the compactified piece in type IIB theory. So instead of ridiculous numbers of dimensions in some arbitrary classical space, we just have dimensions of Hilbert spaces.
Later on I might discuss how one can rewrite this entanglement measure for three qubits in terms of symmetric $3 \times 3$ matrices with entries dependent on only 6 of the 8 amplitudes. Of course, Carl Brannen used similar operators in his paper on the hadron masses, but this paper was rejected due to the unfortunate circumstance that it had almost nothing to do with QCD.