Entanglement Negativity of Spin-Orbit Correlations in a general Qubit-Qudit Setup
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911103229886464 |
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| author | Agrawal, Sanskriti Abir, Raktim |
| author_facet | Agrawal, Sanskriti Abir, Raktim |
| contents | We present the complete eigenvalue spectrum of the partially transposed density matrix for a pure bipartite quantum state acting on a generic $2 \otimes n$ Hilbert space. The spectrum contains four non-zero eigenvalues, as, \begin{eqnarray} λ_{1,2}=\pm \sqrt{A}, ~~~ λ_{3,4}= \frac{1}{2}(1\pm\sqrt{1-4 A}), \nonumber \end{eqnarray} where $A$ is the determinant of the reduced density matrix (traced over the larger subspace). As $0 \leqslant A \leqslant1/4$, only one is negative among the four non-trivial eigenvalues. Within this qubit-qudit framework, we further studied the negativity as a measure of entanglement for the case of spin-orbit correlation of partons inside a proton. The entanglement negativity for spin-orbit correlations is found to be related to the gluon helicity PDF and the Hermitian angle of the associated Hilbert space for linearly polarized protons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21048 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entanglement Negativity of Spin-Orbit Correlations in a general Qubit-Qudit Setup Agrawal, Sanskriti Abir, Raktim High Energy Physics - Phenomenology Nuclear Theory Quantum Physics We present the complete eigenvalue spectrum of the partially transposed density matrix for a pure bipartite quantum state acting on a generic $2 \otimes n$ Hilbert space. The spectrum contains four non-zero eigenvalues, as, \begin{eqnarray} λ_{1,2}=\pm \sqrt{A}, ~~~ λ_{3,4}= \frac{1}{2}(1\pm\sqrt{1-4 A}), \nonumber \end{eqnarray} where $A$ is the determinant of the reduced density matrix (traced over the larger subspace). As $0 \leqslant A \leqslant1/4$, only one is negative among the four non-trivial eigenvalues. Within this qubit-qudit framework, we further studied the negativity as a measure of entanglement for the case of spin-orbit correlation of partons inside a proton. The entanglement negativity for spin-orbit correlations is found to be related to the gluon helicity PDF and the Hermitian angle of the associated Hilbert space for linearly polarized protons. |
| title | Entanglement Negativity of Spin-Orbit Correlations in a general Qubit-Qudit Setup |
| topic | High Energy Physics - Phenomenology Nuclear Theory Quantum Physics |
| url | https://arxiv.org/abs/2505.21048 |