Entanglement entropy in the scattering process

Jinbo Fan, Xuanting Ji, Xi-Jun Ren

Jinbo Fan, Gao-Ming Deng, Xi-Jun Ren

In this paper, we study the entanglement property of a four-particle system. In this system, two initially entangled electrons A and C are scattered by two uncorrelated positrons B and D, respectively. We calculate the entanglements among the particles both before and after the double QED scattering ($AB\ensuremath{\rightarrow}AB,CD\ensuremath{\rightarrow}CD$). We find that the change of entanglement entropy between subsystems A and B during the scattering process is proportional to the total cross section, ${\ensuremath{\sigma}}_{\mathrm{tot}}={\ensuremath{\sigma}}_{AB}\ifmmode\times\else\texttimes\fi{}{\ensuremath{\sigma}}_{CD}$. Even though there is no direct interaction between subsystems A and C (or B and D), the scattering process induces entanglement change among them which is also proportional to ${\ensuremath{\sigma}}_{\mathrm{tot}}$. This result shows some kind of entanglement sharing property in multipartite system. In order to further investigate the entanglement sharing, we calculate the entanglement monotones that quantify the genuine multipartite entanglement in a multipartite system. For our chosen scattering process, ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, however, we find that the outgoing state is a W-type four-partite entangled state that has no genuine four-partite entanglement.

Gregory Levine

Shigenori Seki, I.Y. Park, Sang-jin Sin A

In a scattering process, the final state is determined by an initial state and an S-matrix. We focus on two-particle scattering processes and consider the entanglement between these particles. For two types initial states, i.e., an unentangled state and an entangled one, we calculate perturbatively the change of entanglement entropy from the initial state to the final one. Then we show a few examples in a field theory and in quantum mechanics.

K. Mishima, Michitoshi Hayashi, S. H. Lin

Ian Low, Z.W. Yin

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.