Pure spinors, impure spinors and quantum mechanics

Book chapter


Hewitt, M. 2018. Pure spinors, impure spinors and quantum mechanics. in: Dobrev, V. (ed.) Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Springer.
AuthorsHewitt, M.
EditorsDobrev, V.
Abstract

The geometry of spinors in higher dimensional spaces is used to elucidate a potential ambiguity in the concept of a pure quantum state, and a `toroidal entropy is introduced to provide a measure of the geometrical `impurity' of spinors. The geometry of the sub-manifold of geometrically pure spinors is described. The relationship of toroidal entropy with the preparation of a pure quantum state is discussed. It is shown that the toroidal entropy is trivial in 3 dimensions or for a single qubit system, but may be relevant to the physics of general quantum computation. A generalization of these concepts to general Lie group representations is also presented.

KeywordsLie groups; representations; entropy; quantum computing
Year2018
Book titleQuantum Theory and Symmetries with Lie Theory and Its Applications in Physics
PublisherSpringer
Output statusPublished
ISBN9789811327148
Publication dates
Print13 Dec 2018
Publication process dates
Deposited20 Dec 2018
Related URLhttp://theo.inrne.bas.bg/~dobrev/QTS-10.htm
References

1. P.A.M. Dirac, The Principles of Quantum Mechanics, OUP, Oxford (1930).
2. W. Gerlach, O.Stern, Der experimentelle Nachweis der Richtungsquantelung im
Magnetfeld, Zeitschrift fur Physik (1922) 9 349.
3. E.Cartan, The Theory of Spinors, Dover (1966).
4. C.Chevalley, The Algebraic Theory of Spinors and Cli�ord algebras, Springer
(1996).
5. J.P. Serre, Representations lineaires et espaces homognes kahlriens des groupes
de Lie compacts (d'apres Armand Borel et Andre Weil, Seminaire Bourbaki 2,
447.

JournalProceedings of the 10-th International Symposium "Quantum Theory and Symmetries" (QTS10) with 12-th International Workshop "Lie Theory and Its Applications in Physics" (LT12)
Journal citation1, pp. 331-335
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