On the Structure of Abstract H*Algebras
Abstract
Previously we have shown that the topos approach to quantum theory of Doering and Isham can be generalised to a class of categories typically studied within the monoidal approach to quantum theory of Abramsky and Coecke. In the monoidal approach to quantum theory H*algebras provide an axiomatisation of states and observables. Here we show that H*algebras naturally correspond with the notions of states and observables in the generalised topos approach to quantum theory. We then combine these results with the daggerkernel approach to quantum logic of Heunen and Jacobs, which we use to prove a structure theorem for H*algebras. This structure theorem is a generalisation of the structure theorem of Ambrose for H*algebras the category of Hilbert spaces.
 Publication:

arXiv eprints
 Pub Date:
 March 2018
 DOI:
 10.48550/arXiv.1803.00705
 arXiv:
 arXiv:1803.00705
 Bibcode:
 2018arXiv180300705D
 Keywords:

 Computer Science  Logic in Computer Science;
 Quantum Physics
 EPrint:
 In Proceedings QPL 2017, arXiv:1802.09737