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 dagger-kernel approach to quantumlogic 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.
Original language | English |
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Pages (from-to) | 197-208 |
Number of pages | 12 |
Journal | Electronic Proceedings in Theoretical Computer Science, EPTCS |
Volume | 266 |
DOIs | |
Publication status | Published - 27 Feb 2018 |
Event | 14th International Conference on Quantum Physics and Logic and IQSA Quantum Structures Workshop - Nijmegen, Netherlands Duration: 3 Jul 2017 → 7 Jul 2017 |
Keywords
- generalised topos approach
- quantum theory
- dagger-kernel approach
- h*-algebras