Shapes of Quantum States

Details Shapes of Quantum States Shapes of Quantum States

2003-06-02

arxiv.org/abs/quant-ph/0306013v1

Journal of Physics A37, 251-257 (2004)

Physics

Quantum Physics

Submitted to Proc. R. Statist. Soc

Scientific paper

10.1088/0305-4470/37/1/017

The shape space of k labelled points on a plane can be identified with the space of pure quantum states of dimension k-2. Hence, the machinery of quantum mechanics can be applied to the statistical analysis of planar configurations of points. Various correspondences between point configurations and quantum states, such as linear superposition as well as unitary and stochastic evolution of shapes, are illustrated. In particular, a complete characterisation of shape eigenstates for an arbitrary number of points is given in terms of cyclotomic equations.

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