Entropic lens on stabilizer states

The $n$-qubit stabilizer states are those left invariant by a ${2}^{n}$-element subset of the Pauli group. Clifford group is unitaries which take to states; physically motivated generating set, Hadamard, phase, and controlled-not (cnot) gates comprise gates, impose graph structure on set stabilizers. We explicitly construct these structures, ``reachability graphs,'' at $n\ensuremath{\le}5$. When we consider only reachability graphs separate into multiple, often complicated, connected components. Seeking an understanding entropic states, ultimately built up cnot gate applications two qubits, restricted subgraphs from Hadamard acting $n$ qubits. show how already present qubits embedded more complicated three four argue that no additional types subgraph appear beyond but structures within can grow progressively as qubit number increases. Starting some have entropy vectors not allowed holographic inequalities. comment nature transition between nonholographic graphs.