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arXiv:1906.09696 · Physical review. D/Physical review. D.

Evaluation of entanglement entropy in high energy elastic scattering

R. Peschanski, Shigenori Seki

Published Oct 15, 2019• 50 citations
arXivHTMLPDF

Abstract

Entanglement of the two scattered particles is expected to occur in elastic collisions, even at high energy where they are in competition with inelastic ones. We study how to evaluate quantitatively the corresponding entanglement entropy ${S}_{\mathrm{EE}}$. For this sake, we regularize the divergences occurring in the formal derivation of ${S}_{\mathrm{EE}}$ using a regularization procedure acting on the two-particle Hilbert space of final states. A quantitative application is performed in proton-proton collisions at collider energies, comparing the results of ${S}_{\mathrm{EE}}$ with two different cutoffs and with a volume-regularization obtained by a prescription fixing the finite two-body Hilbert space volume. A significant entanglement is found which persists even at the highest available energies.

DOI
10.1103/physrevd.100.076012

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Entanglement of the two scattered particles is expected to occur in elastic collisions, even at high energy where they are in competition with inelastic ones. We study how to evaluate quantitatively the corresponding entanglement entropy SEE{S}_{\mathrm{EE}}SEE​. For this sake, we regularize the divergences occurring in the formal derivation of SEE{S}_{\mathrm{EE}}SEE​ using a regularization procedure acting on the two-particle Hilbert space of final states. A quantitative application is performed in proton-proton collisions at collider energies, comparing the results of SEE{S}_{\mathrm{EE}}SEE​ with two different cutoffs and with a volume-regularization obtained by a prescription fixing the finite two-body Hilbert space volume. A significant entanglement is found which persists even at the highest available energies.
We are interested in the entanglement entropy of the final state of two particles in an elastic scattering. One can expect that the entanglement is yielded by the interaction between the particles. Within an S-matrix theory, by using the partial wave expansion of the S-matrix elements for two-particle states, we calculate a density matrix in a high energy elastic scattering, and obtain the entanglement entropy formula, which is described by physical observables. In the derivation of this formula, there appear divergences due to the infinite volume of two-particle Hilbert space. In order to avoid such divergences, we suggest a volume-regularization. Then we concretely evaluate the entanglement entropy for proton-proton scattering by using experimental data.
We study the entanglement entropy between the two outgoing particles in an elastic scattering process. It is formulated within an S-matrix formalism using the partial wave expansion of two-body states, which plays a significant role in our computation. As a result, we obtain a novel formula that expresses the entanglement entropy in a high energy scattering by the use of physical observables, namely the elastic and total cross sections and a physical bound on the impact parameter range, related to the elastic differential cross-section.
The scattering cross section is the effective area of collision when two particles collide. Quantum mechanically, it is a measure of the probability for a specific process to take place. Employing wave packets to describe the scattering process, we compute the entanglement entropy in 2-to-2 scattering of particles in a general setting using the S -matrix formalism. Applying the optical theorem, we show that the linear entropy E 2 is given by the elastic cross section σ el in unit of the transverse size L 2 of the wave packet, E 2 ∼ σ el / L 2 , when the initial states are not entangled. The result allows for dual interpretations of the entanglement entropy as an area and as a probability. Since σ el is generally believed, and observed experimentally, to grow with the collision energy s in the high energy regime, the result suggests a “second law” of entanglement entropy for high energy collisions. Furthermore, the Froissart bound places an upper limit on the entropy growth.
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.
We present universal relations between entanglement entropy, which quantifies the quantum correlation between subsystems, and the cross section, which is the primary observable for high-energy particle scattering, by employing a careful formulation of wave packets for the incoming particles. For 2-to-2 elastic scattering with no initial entanglement and subdividing the system along particle labels, we show that both the Rényi and Tsallis entropies in the final states are directly proportional to the elastic cross section in units of the transverse size for the initial wave packets, which is then interpreted as the elastic scattering probability. The relations do not depend on the underlying dynamics of the quantum field theory and are valid to all orders in coupling strengths. Furthermore, computing quantum correlations between momentum and nonkinematic data leads to entanglement entropies expressed as various semi-inclusive elastic cross sections. Our result gives rise to a novel “area law” for entanglement entropy in a two-body system.
We compute the entanglement entropy variation between initial (separable or entangled in the momenta) and final states ΔSEΔS_EΔSE​ in an elastic scattering of a bipartite system composed by two interacting scalar particles. We perform a quantum field theoretical calculation to one loop order and verify that $ΔS_E $ changes as we vary the energy of incoming particles and the coupling strength in a non-trivial way.