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A Categorical Quantum Logic
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2005
"... We define a strongly normalising proofnet calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with biproducts on a given category with an involution. This syntax ca ..."
Abstract

Cited by 21 (4 self)
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We define a strongly normalising proofnet calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with biproducts on a given category with an involution. This syntax can be used to represent and reason about quantum processes.
Delinearizing linearity: projective quantum axiomatics from strong compact closure
 QPL 2005
, 2005
"... ..."
What are the fundamental structures . . .
, 2005
"... I propound a few heresies, and indulge in some dubious speculations. ..."
Completeness and the complex numbers
, 2009
"... The complex numbers are an important part of quantum theory, but are difficult to motivate from a theoretical perspective. We describe a simple formal framework for theories of physics, and show that if a theory of physics presented in this manner satisfies certain completeness properties, then it n ..."
Abstract
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The complex numbers are an important part of quantum theory, but are difficult to motivate from a theoretical perspective. We describe a simple formal framework for theories of physics, and show that if a theory of physics presented in this manner satisfies certain completeness properties, then it necessarily includes the complex numbers as a mathematical ingredient. Central to our approach are the techniques of category theory, and we introduce a new categorytheoretical tool, called the †limit, to prove our results. These †limits can be used to characterize the properties of the †functor on the category of finitedimensional Hilbert spaces, and so can be used as an equivalent definition of the inner product. The technical statement of our main theorem is that in a nontrivial monoidal †category with †limits and a simple tensor unit, in which the selfadjoint scalars are Dedekindcomplete, the scalars are valued in the complex numbers. 1