David Corfield and I came to start something at *EPR paradox*

the entry that used to be titled *quantum mechanics in terms of dagger-compact categories* I have renamed into *finite quantum mechanics in terms of dagger-compact categories* (with a “finite” up front) and I have added to the first sentence the qualifier “finite” and “finite-dimensional” a bunch of times.

I am currently at “Quantum Physics and Logic 2012” in Brussels, and every second speaker advertizes the formalism of what they call “categorical quantum theory”. It’s all fine for the majority of the audience which is all into *quantum information* theory, where one is only interested in shuffling a finite bunch of qbits around, but it is rather misleading from an ordinary perspective on quantum physics. Already the particle on the line is not a finite quantum system.

Hi,

I recently posted a paper that gives, I think, the most general prescription possible for what experiments are. It essentially derives these notions from basic facts about spacetimes. In the paper I give a quasi classical experiment as an example. In this paper, we can actually see another example for quantum systems. Example 5.2 explains that any Frobenius structure on a monoidal category exists because the associated endofunctor $- \otimes B$ is a frobenius monad. Todd gave an answer to a question about the ambidextrous adjuction and pointed out that the category on the other end of the adjunction is the category of B-modules.

I am encouraged by Heunen’s paper. My theory suggests that the adjunciton binds the experiment you are doing to the theory of the system you are probing. In the question with Todd’s responds, I asked about having Hilbert spaces as the base category. $B$, is then an object in Hilb, and the Frobenius structure associated with $B$, I believe is a basis for a hilbert space, which is how we come to know the state of a quantum system, ie measure it. If we take my paper seriously, we expect that at the other end of the adjunction is a theory for the underlying system we are looking at. I am not sure what a B-module is, but I know that module are a generalization of vector spaces, and hence Hilbert spaces.

I would like to open a discussion about how the ambidextrous adjunction points to a theory of Hilbert spaces. Let me know if you agree or disagree.

]]>started *polarized algebraic variety*

at *quantum observable* there used to be just the definition of geometric prequantum observables. I have added a tad more.