On entropy and complexity of coherent states
Abstract
Consanguinity of entropy and complexity is pointed out through the example of coherent states of the group . Both are obtained from the K\"ahler potential of the underlying geometry of the sphere corresponding to the Fubini-Study metric. Entropy is shown to be equal to the K\"ahler potential written in terms of dual symplectic variables as the Guillemin potential for toric manifolds. The logarithm of complexity relating two states is shown to be equal to Calabi's diastasis function. Optimality of the Fubini-Study metric is indicated by considering its deformation.
Cite
@article{arxiv.2407.13327,
title = {On entropy and complexity of coherent states},
author = {Koushik Ray},
journal= {arXiv preprint arXiv:2407.13327},
year = {2025}
}
Comments
14 pages. Rewritten to include the most general case of $SL(d+1,\C)$. The deformation equation for the K\"ahler potential is solved numerically for $d>1$. Version to appear in Journal of Geometry and Physics