Isospectral majorization and isoperimetric inequalities for coherent states on the Bloch sphere
This paper establishes an isospectral version of the Lieb-Solovej inequality for coherent states, demonstrating that rearranging a density operator's eigenvalues in decreasing order along the monomial basis maximizes convex functionals of its Husimi function and Wehrl entropy, while also proving that spherical caps maximize Ky Fan norms and Schatten sums of Toeplitz operators with indicator symbols, thereby yielding new isoperimetric inequalities without relying on the classical spherical isoperimetric inequality.