Abstract
The geometry of the state space of a finite-dimensional quantum mechanical system, with particular reference to four dimensions, is studied. Many novel features, not evident in the two-dimensional space of a single spin, are found. Although the state space is a convex set, it is not a ball, and its boundary contains mixed states in addition to the pure states, which form a low-dimensional submanifold. The appropriate language to describe the role of the observer is that of flag manifolds.
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Adelman, M., Corbett, J.V. & Hurst, C.A. The geometry of state space. Found Phys 23, 211–223 (1993). https://doi.org/10.1007/BF01883625
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DOI: https://doi.org/10.1007/BF01883625