AI 中文总结
研究了洛伦兹 boost 作用下大质量粒子正则自旋的迹距离收缩，通过刻画反演对称信道锥等方法求解优化问题，实现理想构造，证明无辅助自旋可区分性排序与量子统计后处理顺序无关。
AI 中文摘要
洛伦兹 boost 通过与动量相关的维格纳旋转作用于大质量粒子的正则自旋。我们表明，对于一个固定的观察者 boost，在不确定动量上进行约化可以严格收缩每对自旋态的迹距离，且不会产生从收缩较小的态可降解的信道。对于自旋 1/2，我们首先刻画了由固定维格纳角和横向动量方向生成的精确反演对称信道锥。在此锥内有泡利族$M_\alpha=\operatorname{diag}(1 - \alpha,1 - \alpha,1 - 2\alpha)$，$0\leq\alpha<1/2$。对于$0<\alpha<\beta<1/2$，不同自旋态之间的所有迹距离在$M_\beta$之后比在$M_\alpha$之后严格更小，但唯一的线性后处理因子有负的归一化蔡氏特征值。我们精确求解了所有物理转换器上的优化问题：$\frac{1}{2}\inf_{\Lambda\in\mathrm{CPTP}}\|\Phi_\beta-\Lambda\circ\Phi_\alpha\|_\diamond=\frac{\alpha(\beta-\alpha)}{2 - 3\alpha}$，而反向亏缺为$\beta - \alpha$。理想构造通过纯的、可归一化的五分量动量态的窄包极限实现，明确的微扰和有限测量断层扫描界证明了一组开放的例子。另外，每个非恒等成员都不能嵌入到时间齐次的泡利对角林德布拉德半群中。因此，对所有无辅助自旋可区分性进行排序并不能确定量子统计后处理顺序。
英文摘要
A Lorentz boost acts on the canonical spin of a massive particle through a momentum-dependent Wigner rotation. We show that, for one fixed observer boost, reducing over an uncertain momentum can strictly contract every pairwise spin-state trace distance without producing a channel that is degradable from the less contracted one. For spin $1/2$, we first characterize the exact inversion-symmetric channel cone generated by a fixed Wigner angle and transverse momentum directions. Inside this cone lies the Pauli family $M_α=\operatorname{diag}(1-α,1-α,1-2α)$, $0\leqα<1/2$. For $0<α<β<1/2$, all trace distances between distinct spin states are strictly smaller after $M_β$ than after $M_α$, yet the unique linear post-processing factor has a negative normalized Choi eigenvalue. We solve the optimization over all physical converters exactly: $\frac{1}{2}\inf_{Λ\in\mathrm{CPTP}}\|Φ_β-Λ\circΦ_α\|_\diamond=\frac{α(β-α)}{2-3α}$, whereas the reverse deficiency is $β-α$. Thus the identity dominates the family, while all positive-noise members are pairwise incomparable under CPTP post-processing. The ideal construction is realized as the narrow-packet limit of pure, normalizable five-component momentum states, and explicit perturbation and finite-shot tomography bounds certify an open set of examples. Separately, every nonidentity member fails embedding in a time-homogeneous Pauli-diagonal Lindblad semigroup. Hence ordering all unassisted spin distinguishabilities does not determine the quantum statistical post-processing order.
Comments10 pages, 3 figures. Ancillary verification code included
