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.