Pure spinors, impure spinors and quantum mechanics
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.
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.
|Keywords||Lie groups; representations; entropy; quantum computing|
|Book title||Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics|
|13 Dec 2018|
|Publication process dates|
|Deposited||20 Dec 2018|
1. P.A.M. Dirac, The Principles of Quantum Mechanics, OUP, Oxford (1930).
|Journal||Proceedings 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 citation||1, pp. 331-335|
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