verified 3 stabilizer terms reproduce |cat_5>, checked symbolically
Implied per-copy exponent γ ≤ 0.5283 against a published 0.3962 through the implied H-type exponent log₂χ(catm)/(m−2), no improvement.
χ(|cat5⟩) ≤ 3 from ⟨0|_6 |cat6⟩ proportional to |cat5⟩ applied to the three-term decomposition of |cat6⟩ (Qassim, Pashayan, and Gosset, appendix; Kissinger, van de Wetering, and Vilmart, Section 4.1, draw it in ZX). Exact with their Lemma 3, χ(cat_5) > 2, cited in bounds/cat-m5-lower-3.json. Witness built by research/constructions/qpg_cat.py by projecting the three cat_6 terms, and verified in exact arithmetic. Implied H-type exponent log_2(3)/3 = 0.5283.
Qassim, Pashayan, and Gosset · arXiv:2106.07740 · literature
{
"schema_version": "0.1",
"orbit": "cat",
"m": 5,
"direction": "upper",
"rank": 3,
"provenance": {
"author": "Qassim, Pashayan, and Gosset",
"reference": "arXiv:2106.07740",
"method": "literature",
"date": "2021-06-14",
"github": []
},
"notes": "chi(|cat_5>) <= 3 from <0|_6 |cat_6> proportional to |cat_5> applied to the three-term decomposition of |cat_6> (Qassim, Pashayan, and Gosset, appendix; Kissinger, van de Wetering, and Vilmart, Section 4.1, draw it in ZX). Exact with their Lemma 3, chi(cat_5) > 2, cited in bounds/cat-m5-lower-3.json. Witness built by research/constructions/qpg_cat.py by projecting the three cat_6 terms, and verified in exact arithmetic. Implied H-type exponent log_2(3)/3 = 0.5283.",
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