Geometric Aspects of Quantum State Spaces

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The manifold of pure quantum states can be regarded as a complex projective space endowed with the unitary-invariant Fubini-Study metric.
The physical characteristics of a given quantum system can then be represented by a variety of geometrical structures that can be identified in this manifold.
This talk will review a number of examples of such structures as they arise in the state spaces of spin-1/2, spin-1, spin-3/2, and spin-2 systems, and various types of entangled systems, all of which have fascinating and beautiful geometries associated with them.
The geometric approach offers interesting insights into the nature of quantum systems, and is also useful in the consideration of foundational issues such as those related to the measurement problem.