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

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