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• W1587402570 abstract "Geometric phases are important in quantum physics and are now central to fault-tolerant quantum computation. For spin $1∕2$, the Bloch sphere ${S}^{2}$, together with a U(1) phase, provides a complete SU(2) description. We generalize to $N$-level systems and $mathrm{SU}(N)$ in terms of a $2(Nensuremath{-}1)$-dimensional base space and reduction to a $(Nensuremath{-}1)$-level problem, paralleling closely the two-dimensional case. This iteratively solves the time evolution of an $N$-level system and gives $(Nensuremath{-}1)$ geometric phases explicitly. A complete analytical construction of an ${S}^{4}$ Bloch-like sphere for two qubits is given for the Spin(5) or SO(5) subgroup of SU(4)." @default.
• W1587402570 created "2016-06-24" @default.
• W1587402570 creator A5039891277 @default.
• W1587402570 creator A5034831588 @default.
• W1587402570 date "2006-09-14" @default.
• W1587402570 modified "2023-09-26" @default.
• W1587402570 title "Geometric phase for<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>N</mml:mi></mml:math>-level systems through unitary integration" @default.
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• W1587402570 doi "https://doi.org/10.1103/physreva.74.030304" @default.
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