2008/08/07 by Coecke, Bob, Paquette, Eric Oliver, Perdrix, Simon
#Category Theory (math.CT) #FOS: Mathematics #FOS: Physical sciences #Logic (math.LO) #Quantum Algebra (math.QA) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.0808.1029
This paper contains two new results: 1. We amend the notion of abstract basis in a dagger symmetric monoidal category, as well as its corresponding graphical representation, in order to accommodate non-self-dual dagger compact structures; this is crucial for obtaining a `planar' diagrammatical representation of the induced dagger compact structure as well as for representing many complementary bases within one diagrammatic calculus. 2. We (crucially) rely on these basis structures in a purely diagrammatic derivation of the `quantum state transfer protocol'; this derivation provides interesting insights in the distinct structural resources required for state-transfer and teleportation as models of quantum computing.