XXXIX Workshop on Geometric Methods in Physics | 27.06-3.07.2021 |

IX School on Geometry and Physics | 21-25.06.2021 |

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## Francisco Delgado## Geometry of $SU(2)$ decomposition of quantum information systemsComposed interacting quantum systems with Hilbert spaces of dimension $2^{2m}, m \in {\bf Z^+}$ could be represented on some convenient bases (normally of entangled states) then setting Hilbert sub-spaces of size two stating a $SU(2)$ decomposition in their dynamics (properly $U(1)^{2^{m}-1} \times SU(2)^{2^m}$). This dynamics can be understood as linked paths on $2^m$ Bloch spheres weakly related only via quantum entanglement. Such geometric representation admits several quantum control effects as Evolution loops, Exchange operations among others, exhibiting correlated paths on such sub-spaces. This work presents the last decomposition from a geometric point of view showing how it can be used as a grammar for quantum information almost free from the nature of the physical quantum system. |

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University of Bialystok |

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