Deriving Dagger Compactness

@article{Tull2020DerivingDC,
  title={Deriving Dagger Compactness},
  author={Sean Tull},
  journal={Electronic Proceedings in Theoretical Computer Science},
  year={2020}
}
  • S. Tull
  • Published 11 July 2019
  • Mathematics
  • Electronic Proceedings in Theoretical Computer Science
Dagger compact structure is a common assumption in the study of physical process theories, but lacks a clear interpretation. Here we derive dagger compactness from more operational axioms on a category. We first characterise the structure in terms of a simple mapping of states to effects which we call a 'state dagger', before deriving this in any category with 'completely mixed' states and a form of purification, as in quantum theory. 

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