%0 Generic %1 tsimakuridze2016graph %A Tsimakuridze, Nikoloz %A Gühne, Otfried %D 2016 %K Graph states %R 10.1088/1751-8121/aa67cd %T Graph states and local unitary transformations beyond local Clifford operations %U http://arxiv.org/abs/1611.06938 %X Graph states are quantum states that can be described by a stabilizer formalism and play an important role in quantum information processing. We consider the action of local unitary operations on graph states and hypergraph states. We focus on non-Clifford operations and find for certain transformations a graphical description in terms of weighted hypergraphs. This leads to the indentification of hypergraph states that are locally equivalent to graph states. Moreover, we present a systematic way to construct pairs of graph states which are equivalent under local unitary operations, but not equivalent under local Clifford operations. This generates counterexamples to a conjecture known as LU-LC conjecture. So far, the only counterexamples to this conjecture were found by random search. Our method reproduces the smallest known counterexample as a special case and provides a physical interpretation.

@misc{tsimakuridze2016graph, abstract = {Graph states are quantum states that can be described by a stabilizer formalism and play an important role in quantum information processing. We consider the action of local unitary operations on graph states and hypergraph states. We focus on non-Clifford operations and find for certain transformations a graphical description in terms of weighted hypergraphs. This leads to the indentification of hypergraph states that are locally equivalent to graph states. Moreover, we present a systematic way to construct pairs of graph states which are equivalent under local unitary operations, but not equivalent under local Clifford operations. This generates counterexamples to a conjecture known as LU-LC conjecture. So far, the only counterexamples to this conjecture were found by random search. Our method reproduces the smallest known counterexample as a special case and provides a physical interpretation.}, added-at = {2019-06-27T14:54:55.000+0200}, author = {Tsimakuridze, Nikoloz and Gühne, Otfried}, biburl = {https://www.bibsonomy.org/bibtex/25af51d11832936d5b5e3a75334dabde3/annapappa}, description = {Graph states and local unitary transformations beyond local Clifford operations}, doi = {10.1088/1751-8121/aa67cd}, interhash = {2914fda2cab307ca510b0f634178b3ae}, intrahash = {5af51d11832936d5b5e3a75334dabde3}, keywords = {Graph states}, note = {cite arxiv:1611.06938Comment: 19 pages, 8 figures, v2: final version}, timestamp = {2019-06-27T14:54:55.000+0200}, title = {Graph states and local unitary transformations beyond local Clifford operations}, url = {http://arxiv.org/abs/1611.06938}, year = 2016 }