Are You Sure You See?

I’m visiting the KITP in Santa Barbara because they are having a term long workshop on Topological Phases and Quantum Computation (directed by Sander Bais, Chetan Nayak, and John Preskill.) Unfortunately I won’t be able to stay for the entire workshop. But this isn’t as huge of a blow as it would have been years ago, because, the KITP records all of the talks and puts them online. They can be found here.
Yesterday, T. Sentil gave a talk in which he almost made it through his introduction! Anyway one point which he emphasized is something I have always found fascinating. And that is that topological phases (a loose term which I won’t even try to define) might actually be much more common than is widely thought, but the problem is that we don’t have the tools to see them! From the perspective of quantum error correcting codes, this seems fairly natural. In a quantum error correcting code, local probes without at least a global analysis, can not reveal the information encoded into a quantum error correcting code. Indeed if local probes without global analysis could get at our quantum data, then so too could an environment get to this data. Another way to state this is to say that the order parameter for quantum error correcting codes is a big complicated beast whose measurement cannot be done with the simple tools we currently have in our lab.
As a concrete example of this, consider single-molecule molecules. These are crazy molecules which can achieve permanent magnetization through a single molecule effect (usually at fairly low temperatures.) Basically these molecule have a high spin ground state and a high zero-field splitting such that there is a substantial barrier to leaving the high spin ground state. This effect is the result of a collection of interactions among the lower spin systems. What is interesting is the following observation. Take four spin one-half systems and couple them together anti-ferromagnetically with equal couplings between all four systems (mmm, tetrahedrons.) Such a system will have a spin zero ground state which is two fold degenerate. And this two-fold degenerate ground state is actually a single error quantum error detecting code (see quant-ph/0012018)! But why in the world, if you were a chemist, would you go looking for a spin zero molecule. This is the exact opposite of what you would like to find. Further, you won’t be able to see that there is a quantum error detecting code without a knob which allows you to split the degeneracy of this ground state. And doing this is not a trivial task. In short, exactly since we don’t have the tools to observe this effect, we won’t really be interested in it. You need a crazy theorist to tell you that maybe you should think about trying to engineer such a knob onto your system. What use is a crazy theorist except to tell you crazy stories.
Of course, thinking like this, that there might be hidden orders which we are not smart enough to discover is a good way to make yourself paranoid. What might we be hiding from because our glasses are so opaque? Certainly the role of instrumentation in science is one I find fascinating and, I must admit, a bit scary.