Geometry and Symmetric Coherent States of Three Qubits Systems
In this paper, we first generalize the previous results that relate 1- and 2-qubit geometries to complex and quaternionic Möbius transformations respectively, to the case of 3-qubit states under octonionic Möbius transformations. This completes the correspondence between the qubit geometries and the four normed division algebras. Thereby, new systems of symmetric coherent states with 2 and 3 qubits can be constructed by mapping the spin coherent states to their antipodal symmetric ponits on the generalized Bloch spheres via Möbius transformations in corresponding dimensions. Finally, potential applications of the normed division algebras in physics are discussed.
KeywordsQubit geometry Möbius transformation Division algebra Symmetric coherent state
The author thanks Zhiqiang Huang and Jin Yao for helpful discussions. This work is supported in part by Shanghai Normal University under the Grant No. A-6001-15-001487.
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