On the Realization of Quantum State Teleportation in Proton Systems

TL;DR

The work demonstrates that unpolarized proton–proton scattering and unpolarized deuteron breakup can generate strongly entangled proton pairs in Bell states, with the NN transition matrix $M$ becoming dominated by a single Bell component at select energies and angles, enabling near-pure entanglement such as $|\\psi^{-}\\rangle$ or $|\\psi^{+}\\rangle$. By analyzing NN and Nd breakup with realistic potentials and 3N Faddeev equations, the authors map the energy–angle regions where Bell-state formation is favored and show that Coulomb effects do not erase these entangled configurations. Building on this, they propose a teleportation protocol in a three-proton system where scattering one member of an entangled pair off a polarized target transfers the quantum state from proton 1 to proton 3, with clear triple-coincidence and polarization-signature measurements as observables. Their results identify practical energy regimes (e.g., around $10$ MeV and around $150$ MeV for pp; around $350$ MeV for pd FSI) and emphasize the advantage of unpolarized reactions for higher counting rates, outlining a feasible experimental path to test quantum-state teleportation in hadronic systems.

Abstract

We discuss how to generate entangled Bell states of two nucleons using unpolarized nucleon-nucleon scattering or the exclusive deuteron breakup reaction. We follow the the approach of Z. X. Shen et al., arXiv:2510.24325v1 [nucl-th], where Bell states were identified in unpolarized proton-proton elastic scattering. We confirm these results and show that, in the unpolarized proton-deuteron breakup reaction, it is also possible to generate proton-proton entangled Bell states in kinematically complete proton-proton quasi-free scattering (QFS) and final-state interaction (FSI) configurations. We also discuss an experimental setup that, by exploiting such entangled states, could enable the teleportation of quantum mechanical states in a three-proton system. Such an experiment requires triple coincidences among the outgoing nucleons, which precludes the use of entangled Bell states generated with extremely polarized incoming particles. Since counting rates for unpolarized reactions are much higher than for polarized ones, the present results open a pathway toward searching for signatures of quantum state teleportation in hadronic systems.

Figures (36)

• Figure 1: (color online Laboratory-energy dependence of the absolute values of the M-matrix expansion coefficients $|C_{i'i}(\Theta_{c.m.}=90^o)|$ (Eq. (\ref{['eq_6']})) in unpolarized pp and np scattering. Note that at this angle $C_{22}=C_{33}$, and the corresponding curves overlap. The calculations were performed using the AV18 NN potential and a partial-wave set with $j_{max} = 5$. In the legend, the index $i'-i$ of the coefficients and the explanation of the lines are given.
• Figure 2: (color online) The same as in Fig. \ref{['fig1aa']} but for the spin density matrix $\rho_f$ and the coefficients $|\bar{C}_{i'i}(\Theta_{c.m.}=90^o)|$ (Eq. (\ref{['eq_9']})). Note that the absolute values of $|\bar{C}_{23}|$ and $|\bar{C}_{32}|$ are identical and the corresponding curves overlap.
• Figure 3: (color online) Angular distribution of the absolute values of the M-matrix expansion coefficients $|C_{i^,i}|$ (Eq. (\ref{['eq_6']})) in unpolarized pp scattering at $E_{lab}=10$ MeV.
• Figure 4: (color online) Angular distribution of the absolute values of the final spin density matrix expansion coefficients $|\bar{C}_{i^,i}|$ (Eq. (\ref{['eq_9']})) in unpolarized pp scattering at $E_{lab}=10$ MeV.
• Figure 5: (color online) Same as in Fig. \ref{['fig1']}, but for $E_{lab}=151$ MeV.