{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,7]],"date-time":"2026-06-07T08:50:31Z","timestamp":1780822231708,"version":"3.54.1"},"reference-count":42,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2020,8,7]],"date-time":"2020-08-07T00:00:00Z","timestamp":1596758400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>Graph states, and the entanglement they posses, are central to modern quantum computing and communications architectures. Local complementation \u2013 the graph operation that links all local-Clifford equivalent graph states \u2013 allows us to classify all stabiliser states by their entanglement. Here, we study the structure of the orbits generated by local complementation, mapping them up to 9 qubits and revealing a rich hidden structure. We provide programs to compute these orbits, along with our data for each of the <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>587<\/mml:mn><\/mml:math> orbits up to <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>9<\/mml:mn><\/mml:math> qubits and a means to visualise them. We find direct links between the connectivity of certain orbits with the entanglement properties of their component graph states. Furthermore, we observe the correlations between graph-theoretical orbit properties, such as diameter and colourability, with Schmidt measure and preparation complexity and suggest potential applications. It is well known that graph theory and quantum entanglement have strong interplay \u2013 our exploration deepens this relationship, providing new tools with which to probe the nature of entanglement.<\/jats:p>","DOI":"10.22331\/q-2020-08-07-305","type":"journal-article","created":{"date-parts":[[2020,8,7]],"date-time":"2020-08-07T17:06:15Z","timestamp":1596819975000},"page":"305","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":36,"title":["Mapping graph state orbits under local complementation"],"prefix":"10.22331","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8923-7180","authenticated-orcid":false,"given":"Jeremy C.","family":"Adcock","sequence":"first","affiliation":[{"name":"Quantum Engineering Technology (QET) Labs, H. H. Wills Physics Laboratory & Department of Electrical & Electronic Engineering, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol BS8 1UB, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4445-734X","authenticated-orcid":false,"given":"Sam","family":"Morley-Short","sequence":"additional","affiliation":[{"name":"Quantum Engineering Technology (QET) Labs, H. H. Wills Physics Laboratory & Department of Electrical & Electronic Engineering, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol BS8 1UB, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2479-7424","authenticated-orcid":false,"given":"Axel","family":"Dahlberg","sequence":"additional","affiliation":[{"name":"QuTech - TU Delft, Lorentzweg 1, 2628CJ Delft, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3429-4890","authenticated-orcid":false,"given":"Joshua W.","family":"Silverstone","sequence":"additional","affiliation":[{"name":"Quantum Engineering Technology (QET) Labs, H. H. 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