Entropic lens on stabilizer states

Cynthia Keeler, William Munizzi, Jason Pollack

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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

Original languageEnglish (US)
Article number062418
JournalPhysical Review A
Issue number6
StatePublished - Dec 2022
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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