# 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.

Authors | Hewitt, M. |
---|---|

Editors | Dobrev, 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. |

Keywords | Lie groups; representations; entropy; quantum computing |

Year | 2018 |

Book title | Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics |

Publisher | Springer |

Output status | Published |

ISBN | 9789811327148 |

Publication dates | |

Print | 13 Dec 2018 |

Publication process dates | |

Deposited | 20 Dec 2018 |

Related URL | http://theo.inrne.bas.bg/~dobrev/QTS-10.htm |

References | 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 |

https://repository.canterbury.ac.uk/item/887zx/pure-spinors-impure-spinors-and-quantum-mechanics

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