AI 中文总结
该研究针对去极化信道量子容量阈值，给出首个已证明的正性结果，明确45副本两输入态在特定p值下满足I_c>0，还实现了两个竞争码态正性边界的认证排序。
AI 中文摘要
自1996年以来，人们一直在研究量子比特去极化信道保持正量子容量的噪声阈值，迄今为止的每一次改进——最近的是Agarwal等人的记录——都依赖于相干信息的浮点评估。我们给出了该领域首个已证明的正性结果：一个明确的45副本两输入态A，作为1472字节的见证发布，在精确有理值p=16239/250000=0.064956（按每泡利约定；总错误率3p=0.194868）处具有认证的I_c>0，优于之前报道的最佳数值。由于去极化族在复合下是半群，固定输入的相干信息在[0,1/4]上随p非递增，因此单个认证点可扩展到其下方的整个区间。相同的机制将A和Agarwal等人最强公开态的正性边界限制在分离超过1/25000的不相交有理区间内——据我们所知，这是首个对两个竞争码态的已证明排序。论文中的所有计算主张都可简化为有限的大整数比较列表，可由一个无依赖的数百行验证器检查，其可靠性基于三个独立的半页引理。有效载荷、证书和验证器作为补充工件随论文提供。
英文摘要
The noise threshold below which the qubit depolarizing channel retains positive quantum capacity has been studied since 1996. The classic constructions come with exact finite formulae, but in every reported threshold to date -- most recently the record of Agarwal et al. -- the final step, the sign of the coherent information at the reported point, is a floating-point evaluation. We give the first exact-arithmetic, independently machine-checkable positivity proofs in this regime: an explicit 45-copy rank-two input state $A$, published as a 1,472-byte witness, with certified $I_c > 0$ at the exact rational $p = 16239/250000 = 0.064956$ (per-Pauli convention; total error rate $3p = 0.194868$) -- beyond both the best value printed in the Agarwal et al. paper ($0.064657$) and the strongest state in the same authors' public repository ($\approx 0.064911$), both numerical. Because the depolarizing family is a semigroup under composition, fixed-input coherent information is nonincreasing in $p$ on $[0,1/4]$, so a single certified point extends to the entire interval below it. The same machinery confines the positivity boundaries of $A$ and of the strongest public state of Agarwal et al. to disjoint rational intervals separated by more than $1/25000$ -- to our knowledge the first proven ordering of the positivity boundaries of two explicit competing code states. Every computational claim in the paper reduces to a finite list of big-integer comparisons, checkable by a dependency-free few-hundred-line verifier whose soundness rests on three self-contained half-page lemmas. Payloads, certificates, and verifier accompany the paper as a supplementary artifact.
Comments13 pages, 2 tables. v2: expanded attribution and related work; clarified claim scope and evidence taxonomy; certified bound unchanged. Verification artifact: DOI 10.5281/zenodo.21962925
