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Graph States Under the Action of Local Clifford Group in Non-Binary Case

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arxiv quant-ph/0610267 v2 pith:V6YUS26B submitted 2006-10-31 quant-ph

Mohsen Bahramgiri , Salman Beigi This is my paper · ORCID
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Graph states are well-entangled quantum states that are defined based on a graph. Of course, if two graphs are isomorphic their associated states are the same. Also, we know local operations do not change the entanglement of quantum states. Therefore, graph states that are either isomorphic or equivalent under the local Clifford group have the same properties. In this paper, we first establish a bound on the number of graph states which are neither isomorphic nor equivalent under the action of local Clifford group. Also, we study graph states in non-binary case. We translate the action of local Clifford group, as well as measurement of Pauli operators, into transformations on their associated graphs. Finally, we present an efficient algorithm to verify whether two graph states, in non-binary case, are locally equivalent or not.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Local Equivalences of Graph States

    quant-ph 2025-11 conditional novelty 8.0 of 10

    Graph states are LU-equivalent if and only if they are linked by r-local complementations for some integer r; LU-equivalence is decidable in quasi-polynomial time, and LU=LC holds on at most 19 qubits.

  2. Symmetry-guided constructions of absolutely maximally entangled states in five open cases

    quant-ph 2026-08 conditional novelty 7.0 of 10

    New explicit Hermitian self-dual MDS codes yield AME(12,5), AME(18,11), AME(18,13), and their 17-party projections.

  3. Working with measurement-based computations on qudits

    quant-ph 2026-06 conditional novelty 7.0 of 10

    Simpler qudit flow definition yields O(n^3) flow-finding algorithm and flow-preserving operations for measurement-based quantum computing on prime-dimensional qudits.

  4. Foliated Quantum Error Correction for Qudits

    quant-ph 2026-07 conditional novelty 6.0 of 10

    Any prime-dimensional qudit Pauli code can be foliated into a graph state for fault-tolerant measurement-based quantum computing.

  5. Calibrated hypergraph states: II calibrated hypergraph state construction and applications

    quant-ph 2025-01 conditional novelty 6.0 of 10

    Calibrated hypergraph states over Galois rings generalize weighted hypergraph states, are stabilizer and locally maximally entangleable, and reduce to the weighted class in the qubit case only.

  6. Calibrated hypergraph states: I calibrated hypergraph and multi qudit state monads

    quant-ph 2025-01 conditional novelty 6.0 of 10

    Calibrated hypergraphs and multi-qudit states are shown to form graded Ω monads, providing a categorical foundation for a broad generalization of hypergraph states.

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