Physics – Quantum Physics
Scientific paper
2009-06-25
New J. Phys. 13 (2011) 043016
Physics
Quantum Physics
81 pages, many figures. Significant changes from previous version. The first sections contain a gentle introduction for physic
Scientific paper
10.1088/1367-2630/13/4/043016
This paper has two tightly intertwined aims: (i) To introduce an intuitive and universal graphical calculus for multi-qubit systems, the ZX-calculus, which greatly simplifies derivations in the area of quantum computation and information. (ii) To axiomatise complementarity of quantum observables within a general framework for physical theories in terms of dagger symmetric monoidal categories. We also axiomatize phase shifts within this framework. Using the well-studied canonical correspondence between graphical calculi and symmetric monoidal categories, our results provide a purely graphical formalisation of complementarity for quantum observables. Each individual observable, represented by a commutative special dagger Frobenius algebra, gives rise to an abelian group of phase shifts, which we call the phase group. We also identify a strong form of complementarity, satisfied by the Z and X spin observables, which yields a scaled variant of a bialgebra.
Coecke Bob
Duncan Ross
No associations
LandOfFree
Interacting Quantum Observables: Categorical Algebra and Diagrammatics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Interacting Quantum Observables: Categorical Algebra and Diagrammatics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Interacting Quantum Observables: Categorical Algebra and Diagrammatics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-537671