@article{abramsky_categorical_2007,
	title = {A categorical semantics of quantum protocols},
	url = {http://arxiv.org/abs/quant-ph/0402130},
	abstract = {We study quantum information and computation from a novel point of view. Our approach is based on recasting the standard axiomatic presentation of quantum mechanics, due to von Neumann, at a more abstract level, of compact closed categories with biproducts. We show how the essential structures found in key quantum information protocols such as teleportation, logic-gate teleportation, and entanglement-swapping can be captured at this abstract level. Moreover, from the combination of the --apparently purely qualitative-- structures of compact closure and biproducts there emerge `scalars` and a `Born rule'. This abstract and structural point of view opens up new possibilities for describing and reasoning about quantum systems. It also shows the degrees of axiomatic freedom: we can show what requirements are placed on the (semi)ring of scalars C(I,I), where C is the category and I is the tensor unit, in order to perform various protocols such as teleportation. Our formalism captures both the information-flow aspect of the protocols (see quant-ph/0402014), and the branching due to quantum indeterminism. This contrasts with the standard accounts, in which the classical information flows are `outside' the usual quantum-mechanical formalism.},
	urldate = {2020-09-20},
	journal = {arXiv:quant-ph/0402130},
	author = {Abramsky, Samson and Coecke, Bob},
	month = mar,
	year = {2007},
	note = {arXiv: quant-ph/0402130},
	keywords = {Computer Science - Logic in Computer Science, Mathematical Physics, Mathematics - Category Theory, Quantum Physics},
}

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