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26 November 2020
 
  » arxiv » quant-ph/0402130

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A categorical semantics of quantum protocols
Samson Abramsky ; Bob Coecke ;
Date 18 Feb 2004
Journal Proceedings of the 19th IEEE conference on Logic in Computer Science (LiCS’04). IEEE Computer Science Press (2004)
Subject Quantum Physics; Category Theory; Logic in Computer Science; Mathematical Physics | quant-ph cs.LO math-ph math.CT math.MP
AbstractWe 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.
Source arXiv, quant-ph/0402130
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