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A Categorical Quantum Logic

Samson Abramsky and Ross Duncan

Abstract

We define a strongly normalising proof-net 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.

Journal
Mathematical Structures in Computer Science
Note
Preprint available at http://arxiv.org/abs/quant−ph/0512114
Number
3
Pages
469−489
Volume
16
Year
2006