Concrete Foundations for Categorical Quantum Physics

Question

Referee this paper: arXiv:1012.5910 by Daniel Lehmann

Please use comments to point to previous work in this direction, and reviews to referee the accuracy of the paper. Feel free to edit this submission to summarise the paper (just click on edit, your summary will then appear under the horizontal line)

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Abstract from arxiv: An original presentation of Categorical Quantum Physics, in the line of Abramsky and Coecke, tries to introduce only objects and assumptions that are clearly relevant to Physics and does not assume compact closure. Adjoint arrows, tensor products and biproducts are the ingredients of this presentation. Tensor products are defined, up to a unitary arrow, by a universal property related to transformations of composite systems, not by assuming a monoidal structure. Entangled states of a tensor product define mixed states on the components of the tensor product. Coproducts that fit the adjoint structure are shown to be defined up to a unitary arrow and to provide biproducts. An abstract no-cloning result is proved.

Comments

A comment from @DanielMoskovich:

Me: So he is constructing something aesthetically cleaner, while maintaining the physical output of conventional QM?

Daniel: Not aesthetically clear per se, but with less structure (more abstract). Trying to strip away unnecessary structure and to get at some sort of "essence". This is somehow the goal of all of categorical quantum mechanics, I think; but in Lehmann's approach he can prove a more-or-less-honest no-cloning theorem, which sets him apart to the best of my knowledge.