无相位的魔力：胶子散射中与相位无关的稳定器雷尼熵
Magic without a phase: phase-independent stabilizer Rényi entropy in gluon scattering
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中文总结 AI 辅助
研究胶子散射中与相位无关的稳定器雷尼熵，推广魔力概念，以案例研究不同重数散射，发现3→2散射末态魔力特性、2→3散射软极限情况及对称时魔力变化，且颜色依赖性在熵中消除。
中文摘要 AI 辅助
魔力，也称为非稳定性，衡量量子态在量子计算中的有用性。虽然魔力是相对于计算基的选择来定义的，但在某些物理环境中，可用数据仅在局部相位约定下确定此基。在本文中，我们推广了魔力的概念并以与相位无关的方式对其进行表述，从而定义了广义稳定器雷尼熵。作为一个案例研究，我们考虑更高重数的树级胶子散射，将出射螺旋度解释为量子比特。在这种情况下，螺旋度数据自然地为每个量子比特确定一个局部基，但留下相位模糊性。对于3→2散射，我们发现末态与相位无关的魔力通常大于2→2散射中可达到的最大值。对于2→3散射，我们发现在软极限下接近一个非零的最小值。此外，当三个出射动量变得对称时，魔力仅比软极限值高几个百分点就接近局部最小值。在所有考虑的情况下，颜色依赖性从与相位无关的稳定器雷尼熵中消除。
英文摘要
Magic, also known as non-stabilizerness, measures the usefulness of a quantum state for quantum computation. While magic is defined relative to a choice of computational basis, in some physical settings the available data determine this basis only up to local phase conventions. In this paper, we generalize the notion of magic and formulate it in a phase-independent manner, and hence define a generalized stabilizer Rényi entropy. As a case study, we consider higher-multiplicity tree-level gluon scattering, interpreting the outgoing helicities as qubits. In this setting, the helicity data naturally determine a local basis for each qubit but leave a phase ambiguity. For $3\to 2$ scattering, we find that the final-state phase-independent magic is generically larger than the maximum attainable in $2\to 2$ scattering. For $2 \to 3$ scattering, we find a nonzero minimal value approached in the soft limit. Moreover, when the three outgoing momenta become symmetric, the magic approaches a local minimum only a few percent above the soft-limit value. In all cases considered, the color dependence cancels from the phase-independent stabilizer Rényi entropy.
