verified 6 stabilizer terms reproduce |cat_7>, checked symbolically
Implied per-copy exponent γ ≤ 0.5170 against a published 0.3962 through the implied H-type exponent log₂χ(catm)/(m−2), no improvement.
χ(|cat7⟩) ≤ 6 from ⟨0|_8 |cat8⟩ proportional to |cat7⟩ applied to the six-term contraction that decomposes |cat8⟩ (Qassim, Pashayan, and Gosset, appendix, χ(cat_7) ≤ χ(cat_8) ≤ 6). Witness built by research/constructions/qpg_cat.py by projecting the six cat_8 terms, and verified in exact arithmetic; the six projected terms are linearly independent. Implied H-type exponent log_2(6)/5 = 0.5170.
Qassim, Pashayan, and Gosset · arXiv:2106.07740 · literature
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"author": "Qassim, Pashayan, and Gosset",
"reference": "arXiv:2106.07740",
"method": "literature",
"date": "2021-06-14",
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"notes": "chi(|cat_7>) <= 6 from <0|_8 |cat_8> proportional to |cat_7> applied to the six-term contraction that decomposes |cat_8> (Qassim, Pashayan, and Gosset, appendix, chi(cat_7) <= chi(cat_8) <= 6). Witness built by research/constructions/qpg_cat.py by projecting the six cat_8 terms, and verified in exact arithmetic; the six projected terms are linearly independent. Implied H-type exponent log_2(6)/5 = 0.5170.",
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