AI 中文总结
研究有限群量子参考系噪声的最大经典化，证明表示完备性是量子后处理简化为经典卷积的条件，确定辅助维度，推导缺陷差距，通过共轭表示表征定律可识别性，提供线性规划等，确定性辅助码验证示例。
AI 中文摘要
具有群值未对准的有限量子参考令牌会引发随机酉信道，但最优退化通常是对所有量子后处理的优化。对于有限群\(G\)的酉表示\(U\)，证明了几个条件等价，如\(U\)包含每种不可约类型等。表示完备性是将量子后处理普遍简化为经典卷积的精确载体条件。确定了正交轨道和不变校准种子的最小辅助维度。对于不完全载体，推导了精确的条件期望距离和明确的量子 - 经典缺陷差距。还通过共轭表示表征了定律可识别性，提供了有限线性规划和决策见证等。确定性辅助码重现了有限群示例并进行了数值回归检验。
英文摘要
A finite quantum reference token with group-valued misalignment induces a random-unitary channel, but optimal degradation is generally an optimization over all quantum post-processings. For a unitary representation U of a finite group G, we prove that the following conditions are equivalent: U contains every irreducible type; one ancilla-assisted input has an orthonormal G-orbit; signed group measures embed isometrically into channels in diamond norm; and, for every pair of noise laws p,q, $\inf_{Λ\in\mathrm{CPTP}} \frac{1}{2}\|Φ_q^U-Λ\circΦ_p^U\|_\diamond =\min_{r\in\mathcal{P}(G)}\frac{1}{2}\|q-r*p\|_1$. Thus representation completeness is the exact carrier condition for universal reduction of quantum post-processing to classical convolution. We determine the minimum ancilla dimensions for an orthogonal orbit and for an invariant calibration seed. For an incomplete carrier, with visible Plancherel dimension S(U), we derive the exact conditional-expectation distance $\frac{1}{2}\|\operatorname{id}-Φ_u^U\|_\diamond=1-1/S(U)$ and an explicit quantum--classical deficiency gap. For irreducible carriers the deficiency is obtained in closed form; the faithful two-dimensional representation of $S_3$ yields an exact ten-percent reduction relative to classical convolution. We also characterize law identifiability through the conjugation representation, provide finite linear programs and decision witnesses, and establish both a finite-dimensional obstruction and stable visible-band reconstruction for infinite compact groups. Deterministic ancillary code reproduces the finite-group examples and numerical regression checks.
Comments13 pages, 1 figure. Ancillary verification code included
