Some properties of Grassmannian $U(4)/U{(2)}^{2}$ coherent states and an entropic conjecture

We analyze mathematical and physical properties of a previously introduced (Calixto and Perez-Romero 2014 J. Phys. A: Math. Theor. 47023027) family of U(4) coherent states (CS). They constitute a matrix version of standard spin U(2) CS when we add an extra (pseudospin) dichotomous degree of freedom: layer, sublattice, two-well, nucleon, etc. Applications to bilayer quantum Hall systems at fractions of filling factor are discussed, where Haldane's sphere picture is generalized to a Grassmannian picture. We also extend Wehrl's definition of entropy from Glauber to Grassmannian CS and state a conjecture on the entropy lower bound.