The Bloch-Vector Space for N-Level Systems: the Spherical-Coordinate Point of View

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  • Gen Kimura
    Department of Physics, Waseda University, Tokyo 169–8555, Japan
  • Andrzej Kossakowski
    Institute of Physics, Nicolaus Copernicus University, Toruń 87–100, Poland

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<jats:p> Bloch-vector spaces for N-level systems are investigated from the spherical-coordinate point of view in order to understand their geometrical aspects. We present a characterization of the space by using the spectra of (orthogonal) generators of SU (N). As an application, we find a dual property of the space which provides an overall picture of the space. We also provide three classes of quantum-state representations based on actual measurements and discuss their state-spaces. </jats:p>

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