2009/09/05 by Spencer D. Stirling, Stirling, Spencer D., Yong-Shi Wu +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #math-ph #math.CT #math.LO #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.0909.0988
74 pages, Part I
arxiv created 2009/09/05 · openalex publication_date 2009/09/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is the first paper in a series where we generalize the Categorical Quantum Mechanics program (due to Abramsky, Coecke, et al) to braided systems. In our view a uniform description of quantum information for braided systems has not yet emerged. The picture is complicated by a diversity of examples that lacks a unifying framework for proving theorems and discovering new protocols. We use category theory to construct a high-level language that abstracts the quantum mechanical properties of braided systems. We exploit this framework to propose an axiomatic description of braided quantum information intended for topological quantum computation. In this installment we first generalize the primordial Abramsky-Coecke "quantum information flow" paradigm from compact closed categories to right-rigid strict monoidal categories. We then study dagger structures for rigid and/or braided categories and formulate a graphical dagger calculus. We then propose two generalizations of strongly compact closed categories. Finally we study partial traces in the context of dagger categories.