Perfectness of the Pauli Commutation Graph Resolves the Triply Efficient Shadow Tomography Conjecture
Year: 2026
Type: article
Abstract: Proves that the fractional chromatic number of the Pauli commutation graph equals the clique number for Fano-sector states (k=7 fermions), resolving Conjecture 1.1 of King-Gosset-Kothari-Babbush (SODA 2025) in this sector. The proof uses total-variation stratification of the magic resource theory: stabiliser states (TV=1) admit O(1/delta^2) shadow complexity; genuinely magic states require Omega(d) samples. The Fano sector is the unique perfect case among odd-cycle commutation graphs.
Author: Buckley, Ian R. C.
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167699447
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