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arXiv:2601.14145

On the Realization of Quantum State Teleportation in Proton Systems

Henryk Witała

Published Jan 20, 2026• 0 citations
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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.

DOI
10.48550/arxiv.2601.14145

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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.
We discuss the feasibility of quantum spin-state teleportation in a three-proton system at an energy of 151 MeV, where, similarly to the low-energy case, a single Bell-state term dominates the proton-proton scattering matrix. We find that, in contrast to the low-energy regime, where unpolarized proton-proton scattering produces strongly entangled outgoing proton pairs, at higher energies a pair of protons, each with an energy of 151151151~MeV, must be produced in an unpolarized, exclusive proton-deuteron breakup reaction under complete final-state-interaction kinematics. The subsequent interaction of one of the entangled protons with a polarized hydrogen target triggers, as in the low-energy case, the teleportation process, whereby the polarization of the target proton is transferred to the second member of the entangled pair within the very narrow angular region of strong entanglement centered around a laboratory scattering angle of 45∘45^\circ45∘. We also find that scattering one member of a strongly correlated proton pair forming a Bell state from an unpolarized hydrogen target leads to Einstein-Podolsky-Rosen-like correlations between the polarization of the scattered proton and that of the unscattered second entangled proton. The polarization of the scattered proton varies with its scattering angle. An identical polarization, following the angular dependence of thepolarization of the first proton, is induced in the second member of the pair, whose initial polarization was zero and whose momentum remains unchanged. The sign of the polarization of the second proton is determined by the sign of the spin correlation in the Bell state.
We discuss the peculiarities of scattering in a three-proton system induced by the presence of an entangled proton-proton Bell-like state in the initial configuration. We formulate the problem using the standard spin formalism of nuclear physics in order to follow in detail the reaction pathways leading to the teleportation of a quantum-mechanical state within this system. By performing numerical simulations of the system and calculations based on a realistic nucleon-nucleon potential, we evaluate the relevant spin observables and search for a simple, experimentally feasible signal that could provide clear evidence of quantum teleportation. For the case in which proton 2, belonging to the entangled proton pair 23, interacts with hydrogen target 1, thereby triggering the teleportation process, we find clear evidence of teleportation through measurements of the final polarization of proton 3', even for small values of the polarization of target proton 1. The dominant component of this polarization is transferred almost entirely from target proton 1 to proton 3 in the angular region characterized by strong entanglement. For an unpolarized target proton 1, quantum teleportation is no longer possible. The only unambiguous signature of the residual quantum correlations would be provided by measurements of the spin correlations within the strongly entangled final-state proton pair 1'2'. Indirect evidence may also be obtained from measurements of the polarization of proton 2' in the final state, although the corresponding effectis relatively weak.
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We investigate polarization states of the outgoing neutron-proton (npnpnp) pair in elastic polarized neutron and proton scattering, aiming to find unambiguous evidence for entanglement of their spin states. To obtain complete information about these states, we calculate, using the high precision nucleon-nucleon potential AV18, the final polarizations of the neutron and proton as well as their spin correlation coefficients, which unequivocally define the corresponding spin density matrix. We compute all terms contributing to polarizations and spin correlations, e.g. not only induced polarizations and correlations resulting from unpolarized npnpnp scattering, but also contributions from single polarization and correlation transfers from individual polarized incoming nucleons, and, for the first time, allotment to both quantities stemming from a doubly spin polarized initial state. We find that for the most part the final spin states are statistical mixture of states.The only pure states occur for highly polarized incoming neutrons and protons with maximal polarizations. By quantifying the degree of entanglement through entanglement power and concurrence, we observed that the entanglement of impure final states increases with energy. Among the pure spin states resulting from incoming states with maximal neutron and proton polarizations, we found, at Elab=100E_{lab}=100Elab​=100~MeV, cases of strongly entangled Bell-type states with only a small admixture of entanglement-spoiling contributions.
Entanglement is a key resource in quantum information science, yet its properties and applications in nuclear systems remain largely unexplored. Here, using proton-proton scattering as a quantum laboratory, we report the emergence of a near-pure Bell-triplet state at a laboratory energy of 151 MeV and a center-of-mass scattering angle of 90°. In this unique kinematic regime, the scattering amplitude functions as a transition operator connecting distinct Bell states. Building upon this emergent resource, we propose a quantum teleportation protocol for proton spins, exploiting the intrinsic Hamiltonian of the strong interaction to perform the requisite Bell measurement effectively. These findings effectively bridge few-body nuclear physics and quantum technology, establishing proton-proton scattering as both a source of high-fidelity entanglement and a natural processor for quantum information.
Abstract Generation of an entangled spin state as a result of a low-energy elastic collision of two protons is considered. The scattering process is described by a theoretical model that is in good agreement with the available experimental data on the angular differential cross sections of proton–proton collisions at low energies. The entanglement of the spin state of final protons as a function of the scattering angle is analyzed using Bell’s inequality and pair concurrence. The numerical results for different values of the collision energy are compared with the results without considering nuclear forces. It is shown that nuclear interaction significantly enhances the effects of spin entanglement.