For any pure qubit-qudit state, the negativity of the partial transpose equals the square root of the determinant of the two-by-two reduced density matrix, which the paper applies to spin-orbit entanglement in protons.
What remaines is to havec + andc − orthogonal,i.e., ⟨c+,c−⟩=0
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Entanglement Negativity of Spin-Orbit Correlations in a general Qubit-Qudit Setup
For any pure qubit-qudit state, the negativity of the partial transpose equals the square root of the determinant of the two-by-two reduced density matrix, which the paper applies to spin-orbit entanglement in protons.