AI 中文总结
该研究对比实验室基矢与螺旋度基矢下QED和电弱过程的魔力产生情况，发现弱混合角接近魔力产生最小的值，且超相对论下螺旋度基矢魔力产生更少。
AI 中文摘要
量子魔力（又称非稳定度）是与量子系统计算优势相关的量子资源。在高能碰撞中，量子电动力学（QED）在产生魔力方面效率低下，而弱混合角这一自然基本常数的取值，恰好接近带电轻子散射中魔力产生量最小的值。这些观测是在实验室（lab）基矢下完成的，该基矢中自旋沿入射束轴投影。另一种选择是螺旋度基矢，其中自旋沿每个粒子的运动方向投影。这两种基矢之间的变换通常不是克利福德（Clifford）操作，因此会改变魔力的数量。我们详细研究了QED和电弱过程在两种基矢下的魔力产生情况，并将这些结果与基矢不变的非局域魔力进行比较。在超相对论极限下，由于螺旋度选择定则，螺旋度基矢中的魔力产生量通常更小，而在非相对论区域，实验室基矢通常产生的魔力更少。我们利用幺正算子的线性组合给出了超相对论Bhabha振幅的电路实现，并表明在一般散射角下，实验室基矢构造包含更多的T门数量。有趣的是，在两种基矢下，物理弱混合角都接近使魔力产生量最小的值。
英文摘要
Quantum magic, or nonstabilizerness, is a quantum resource associated with computational advantage in quantum systems. In high energy collisions, Quantum Electrodynamics (QED) is inefficient at generating magic while the weak mixing angle, a fundamental constant of nature, sits near a value that minimizes magic production in charged-lepton scattering. These observations were made in the laboratory (lab) basis, in which spin is projected along the incoming beam axis. An alternative choice is the helicity basis, in which spin is projected along the direction of motion of each particle. The transformation between these two bases is, in general, not a Clifford operation and therefore can change the amount of magic. We present a detailed study of magic production in both bases for QED and electroweak processes, and compare these results with the basis-invariant non-local magic. In the ultra-relativistic limit, magic production is generally smaller in the helicity basis due to helicity selection rules, while the lab basis generally yields less magic in the non-relativistic regime. We provide circuit realizations of the ultra-relativistic Bhabha amplitudes using linear combinations of unitaries and show that the lab basis construction contains a larger $T$-gate count at generic scattering angles. Interestingly, in both bases the physical weak mixing angle lies close to the value that minimizes magic production.
Comments37 pages, 8 figures
