NUMERICAL SHADOW

For any square matrix $A$ of dimension $N$, one defines its numerical shadow as a probability distribution $P_A(z)$ on the complex plane, supported in the numerical range $W(A)$,... [1]T. Gallay and D. Serre, "Numerical measure of a complex matrix," Communications on Pure and Applied Mathematics, vol. 65, no. 3, pp. 287-336, 2012, [Online]. Available at: https://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.20374... Here $\mu(\psi)$ denotes the unique, unitarily invariant (Fubini-Study) measure on the set $\Omega_N$ of $N$-dimensional pure quantum states. In other words the shadow $P$ of matrix $A$ at a given point $z$ characterizes the likelihood that the expectation value of $A$ among a random pure state is equal to $z$.