Coherent numerical shadow

Coherent numerical shadow of a matrix $A$ is defined as a probability distribution $P_A(z)$ on the complex plane, supported on the coherent numerical range $W^{\mathrm{ent}}(A)$. $P_A(z):={\int }_{\mathrm{\Omega }}\mathrm{d}\mu (\psi )\delta (z-⟨\psi |A|\psi ⟩),$ where $\mu (\psi )$ denotes the unique unitarily invariant (Fubini-Study) measure on the set of $SU(2)$ coherent states.