TBNQuantum
What are local complementations, really?
Publication: quant-ph updates on arXiv.org
Author: Kenneth Goodenough
Source published: 09/11/2026, 05:00:00 UTC
Briefing created: 09/11/2026, 07:10:31 UTC
Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 09/11/2026, 05:13:24 UTC.
Briefings
This paper introduces local complementations as a fundamental operation in graph theory, showing they are equivalent to switching matroid bases of stabilizer states. The authors demonstrate how this perspective simplifies proofs regarding graph properties like vertex-minors and Pauli measurement statistics. Key findings include the identification of Bouchet as a foundational reference and the application of multimatroids to quantum information theory.
Key points
- Local complementations replace the induced neighborhood of a vertex with its complement in a graph G.
- This operation is equivalent to switching matroid bases of stabilizer states, revealing structural properties of graph states.
Context
Local complementations are a fundamental notion in graph state theory, originally linked to Clifford equivalence. This paper provides a new framework using matroid bases to understand these operations, simplifying prior proofs and introducing applications to multimatroids in quantum information theory.
Limitations
The evidence is limited to a single preprint from arXiv. No experimental data, specific numerical results, or named researchers beyond Bouchet are provided. The paper does not contain citations to other sources, and the connection between matroid switching and Clifford equivalence remains theoretical without further verification.
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