Claims made recently in the CERN Courier that string theory can be applied to Quantum Information Theory (see here) are being followed up with a new paper entitled Four-qubit entanglement from string theory which appears to claim that, despite what some might think, string theory is falsifiable since it makes experimentally testable predictions about Quantum Information Theory:
Falsifiable predictions in the fields of high-energy physics or cosmology are hard to come by, especially for ambitious attempts, such as string/M-theory, to accommodate all the fundamental interactions. In the field of quantum information theory, however, previous work has shown that the stringy black hole/qubit correspondence can reproduce well-known results in the classification of two and three qubit entanglement. In this paper this correspondence has been taken one step further to predict new results in the less well-understood case of four-qubit entanglement that can in principle be tested in the laboratory.
Previous papers along these lines about the three-qubit case involved some algebra that I referred to as “remarkably obscure”, a comment that “was like waving a red flag in front of a bull” as far as John Baez was concerned, leading him to some expository comments about the subject in his latest This Week’s Finds in Mathematical Physics. About the string theory claims he comments:
Unfortunately, Duff gets a bit carried away. For example, he says that string theory “predicts” the various ways that three qubits can be entangled. Someone who didn’t know physics might jump to the conclusion that this is a prediction whose confirmation lends credence to string theory as a description of the fundamental constituents of nature. It’s not!
Unlike the three-qubit papers, this latest one sticks to mathematics that is not particularly obscure. The mathematics invoked is the quite beautiful subject of the classification of nilpotent orbits in a Lie algebra. I’ve been trying to learn more about some related topics in recent months, having to do with the role of nilpotent orbits in representation theory. Part of this story involves what are now known as “finite W-algebras”, and these have a BRST definition. I’ve been curious about the relation of this to the BRST/Dirac Cohomology relationship I’ve been working on.
The mathematical problem at issue here is that of classifying SL(2,C)4 orbits on the four-fold tensor product of C2. For an exposition of this problem aimed at mathematicians, see these lecture notes by Nolan Wallach. In the new paper, the authors claim that the Kostant-Sekiguchi theorem implies that this classification is the same as that of orbits of SO(4,C) on its Lie algebra, and this latter classification also classifies certain sorts of black holes in supergravity, but I haven’t checked the details of this. It’s a complete mystery to me why the use of the Kostant-Sekiguchi theorem to relate the straight-forward mathematics used in QIT to a black hole classification problem is going to somehow turn string theory into falsifiable, experimentally testable science.