Circle graphs are closed under r-local complementation and bipartite circle graph states correspond one-to-one with planar code states whose MBQC is classically simulable.
The LU-LC conjecture is false
3 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
The LU-LC conjecture is an important open problem concerning the structure of entanglement of states described in the stabilizer formalism. It states that two local unitary equivalent stabilizer states are also local Clifford equivalent. If this conjecture were true, the local equivalence of stabilizer states would be extremely easy to characterize. Unfortunately, however, based on the recent progress made by Gross and Van den Nest, we find that the conjecture is false.
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Geometric study of non-stabilizerness in few-qubit systems via trace distance to the stabilizer polytope, with state sampling, measure comparisons, an analytical expression, facet classification, and a concentration bound linking it to entanglement.
LC-inequivalent graph-state blocks in random Clifford circuits yield distinct entanglement velocities v_E and butterfly velocities v_B, correlated with internal entanglement distribution and graph connectivity.
citing papers explorer
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The Structure of Circle Graph States
Circle graphs are closed under r-local complementation and bipartite circle graph states correspond one-to-one with planar code states whose MBQC is classically simulable.
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A trace distance-based geometric analysis of the stabilizer polytope for few-qubit systems
Geometric study of non-stabilizerness in few-qubit systems via trace distance to the stabilizer polytope, with state sampling, measure comparisons, an analytical expression, facet classification, and a concentration bound linking it to entanglement.
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Graph-State Circuit Blocks control Entanglement and Scrambling Velocities
LC-inequivalent graph-state blocks in random Clifford circuits yield distinct entanglement velocities v_E and butterfly velocities v_B, correlated with internal entanglement distribution and graph connectivity.