verified 6 stabilizer terms reproduce |cat_8>, checked symbolically
Implied per-copy exponent γ ≤ 0.4308 against a published 0.3962 through the implied H-type exponent log₂χ(catm)/(m−2), no improvement.
χ(|cat8⟩) ≤ 6 from ⟨cat_2|_{4,5}(|cat4⟩ ⊗ |cat6⟩) proportional to |cat8⟩ (Qassim, Pashayan, and Gosset, appendix): ⟨cat_2| is a stabilizer state, so the 2 x 3 contracted products of the cat_4 and cat_6 terms are a decomposition. Through χ(T^8) ≤ 2 χ(cat_8) this gives the 12 of their Table 1 at eight copies. Witness built by research/constructions/qpg_cat.py; the six contracted terms are nonzero and linearly independent, and the identity is verified in exact arithmetic. Implied H-type exponent log_2(6)/6 = 0.4308; rank 5 here would give 0.3870 and beat the published exponent.
Qassim, Pashayan, and Gosset · arXiv:2106.07740 · literature
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"reference": "arXiv:2106.07740",
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"notes": "chi(|cat_8>) <= 6 from <cat_2|_{4,5}(|cat_4> (x) |cat_6>) proportional to |cat_8> (Qassim, Pashayan, and Gosset, appendix): <cat_2| is a stabilizer state, so the 2 x 3 contracted products of the cat_4 and cat_6 terms are a decomposition. Through chi(T^8) <= 2 chi(cat_8) this gives the 12 of their Table 1 at eight copies. Witness built by research/constructions/qpg_cat.py; the six contracted terms are nonzero and linearly independent, and the identity is verified in exact arithmetic. Implied H-type exponent log_2(6)/6 = 0.4308; rank 5 here would give 0.3870 and beat the published exponent.",
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