Unit Quaternions and the Bloch Sphere
| Autor: | Wharton, K. B., Koch, D. |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | J. Phys. A: Math. Theor. 48 (2015) 235302 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1751-8113/48/23/235302 |
| Popis: | The spinor representation of spin-1/2 states can equally well be mapped to a single unit quaternion, yielding a new perspective despite the equivalent mathematics. This paper first demonstrates a useable map that allows Bloch-sphere rotations to be represented as quaternionic multiplications, simplifying the form of the dynamical equations. Left-multiplications generally correspond to non-unitary transformations, providing a simpler (essentially classical) analysis of time-reversal. But the quaternion viewpoint also reveals a surprisingly large broken symmetry, as well as a potential way to restore it, via a natural expansion of the state space that has parallels to second order fermions. This expansion to "second order qubits" would imply either a larger gauge freedom or a natural space of hidden variables. Comment: 25 pages, 1 figure; Referee-inspired improvements; accepted for publication in J. Phys. A |
| Databáze: | arXiv |
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