Abstract Treating Coulomb scattering of two free electrons in a stationary approach, we explore the momentum and spin entanglement created by the interaction. We show that a particular discretisation provides an estimate of the von Neumann entropy of the one-electron reduced density matrix from the experimentally accessible Shannon entropy. For spinless distinguishable electrons the entropy is sizeable at low energies, indicating strong momentum entanglement, and drops to almost zero at energies of the order of 10 keV when the azimuthal degree of freedom is integrated out, i.e. practically no entanglement and almost pure one-electron states. If spin is taken into account, the entropy for electrons with antiparallel spins should be larger than in the parallel-spin case, since it embodies both momentum and spin entanglement. Surprisingly, this difference, as well as the deviation from the spin-less case, is extremely small for the complete scattering state. Strong spin entanglement can however be obtained by post-selecting states at scattering angle π/2.

中文翻译：

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电子-电子散射中的纠缠和熵

摘要 在静态方法中处理两个自由电子的库仑散射，我们探索了相互作用产生的动量和自旋纠缠。我们表明，特定的离散化提供了从实验上可访问的香农熵中对单电子约化密度矩阵的冯诺依曼熵的估计。对于无自旋的可区分电子，熵在低能量时相当大，表明有很强的动量纠缠，当方位角自由度被积分时，熵在 10 keV 量级的能量下下降到几乎为零，即实际上没有纠缠和几乎纯单电子状态。如果考虑自旋，具有反平行自旋的电子的熵应该大于平行自旋情况下的熵，因为它体现了动量和自旋纠缠。出奇，对于完全散射状态，这种差异以及与无自旋情况的偏差非常小。然而，通过在散射角 π/2 处进行后选择状态，可以获得强自旋纠缠。