Quantum measurements without sums

@article{Coecke2007QuantumMW,
  title={Quantum measurements without sums},
  author={Bob Coecke and Dusko Pavlovic},
  journal={arXiv: Quantum Physics},
  year={2007}
}
Sums play a prominent role in the formalisms of quantum me- chanics, whether for mixing and superposing states, or for composing state spaces. Surprisingly, a conceptual analysis of quantum measurement seems to suggest that quantum mechanics can be done without direct sums, expressed entirely in terms of the tensor product. The corresponding axioms define clas- sical spaces as objects that allow copying and deleting data. Indeed, the infor- mation exchange between the quantum and the classical… 
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