The entropy cones of $W_N$ and $W_N^d$ states

Abstract: The quantum entropy cones (QEC) for $W_N$ states of qubits and $W_N^d$ states of qudits are computed. These cones emerge as symmetrized quantum entropy cones (SQEC) for arbitrary $N$ and $d$. Directed graph models are presented which describe the SQEC for $W_N$ states and $W_N^d$ states. Monogamous mutual information (MMI) is violated for all $N>3$.