Spin entanglement signatures of proton from a light-front Hamiltonian

Abstract

Quantum entanglement provides a quantitative probe of the internal structure of hadrons and offers a sensitive means to study the quantum correlation in the hadron wave functions. For baryons, the spin state of the three valence quarks forms a tripartite qubit system, whose entanglement structure can be characterized by the four classes of three-qubit states. In this work, we compare the proton spin entanglement obtained from Basis Light-Front Quantization (BLFQ) with that from a quark-diquark model. By analyzing both bipartite and tripartite entanglement, we find that the quark-diquark model yields a substantially more entangled spin state than the BLFQ wave function in the valence Fock sector. This difference mainly originates from the larger W-type and Bell-type entanglement in the quark-diquark model. Within BLFQ, larger stronger coupling constant and smaller quark mass drive the spin correlation among the valence quarks towards an effective quark-diquark configuration with an active $d$ quark and a correlated $uu$ pair.

Figures (3)

• Figure 1: The comparison of bipartite entanglement and tripartite entanglement between the spin states from three different models: the quark-diquark model Maji:2016yqo, the BLFQ model Xu:2021wwj, and the $\mathrm{SU\left(6\right)}$ quark model. The three spin sectors from the quark-diquark model are included as well (dots and dashed lines in light colors). The main plot shows the entanglement entropy of one parton with the remaining two partons of the proton states from different models, and the inset shows the $\pi$-tangle among the three partons.
• Figure 2: The comparison of the tripartite entanglement between the BLFQ spin states Xu:2021wwj with different parameters and those from the quark-diquark model Maji:2016yqo. The green dots are the values of the triangle measure $F_{123}$ and the orange dots are the values of the $\pi-$tangle. The dashed lines indicate the $F_{123}$ and $\pi$-tangle values of the $d-uu$ quark-diquark state $\left|dA^1\right\rangle$, see text for details. The subplots: (a) Tripartite entanglement with the strong coupling constant $\alpha_{s}=1.0$, $1.1$, $1.2$ and quark mass $m_\mathrm{q/k}=0.3\,\rm{GeV}$. (b) Tripartite entanglement with the quark mass $m_{\mathrm{q/k}}=0.25\,\mathrm{GeV}$, $0.3\,\mathrm{GeV}$, $0.35\,\mathrm{GeV}$ and the strong coupling constant $\alpha_s=1.2$.
• Figure 3: The comparison of the bipartite entanglement entropy between the BLFQ spin states Xu:2021wwj with different parameters and those from the quark-diquark model Maji:2016yqo. The dots and dashed lines indicate the entanglement entropy of the quark-diquark spin state and the three individual spin sectors, see text for details. The subplots: (a) Entanglement entropy with strong coupling constant $\alpha_{s}=1.0$, $1.1$, $1.2$ and the quark mass $m_\mathrm{q/k}=0.3\,\rm{GeV}$. (b) Entanglement entropy with the quark mass $m_{\mathrm{q/k}}=0.25\,\mathrm{GeV}$, $0.3\,\mathrm{GeV}$, $0.35\,\mathrm{GeV}$ and strong coupling constant $\alpha_s=1.2$.