As the age of blogging rolls on, people seem to be more and more enthusiastic about the prospects of string theory. Today kneemo

highlights a new

paper by Kallosh. Mottle continues to

entertain with links to F theory, for experts only, and of course

Woit somehow manages to continuously whine.

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.