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.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.

arXiv:2112.04254Physical review. D/Physical review. D.Dec 23, 202112 citations

Entanglement distribution in Bhabha scattering with an entangled spectator particle

Massimo Blasone A, Gaetano Lambiase, Bruno Micciola

We analyze how entanglement is generated and distributed in a Bhabha scattering process $({e}^{\ensuremath{-}}{e}^{+}\ensuremath{\rightarrow}{e}^{\ensuremath{-}}{e}^{+})$ at tree level. In our setup an electron $A$ scatters with a positron $B$ , which is initially entangled with another electron $C$ (spectator), that does not participate directly to the process. We find that the QED scattering generates and distributes entanglement in a nontrivial way among the three particles; the correlations in the output channels $AB$ , $AC$ , and $BC$ are studied in detail as functions of the scattering parameters and of the initial entanglement weight. Although derived in a specific case, our results exhibit some general features of other similar QED scattering processes, for which the extension of the present analysis is straightforward.We analyze how entanglement is generated and distributed in a Bhabha scattering process $({e}^{\ensuremath{-}}{e}^{+}\ensuremath{\rightarrow}{e}^{\ensuremath{-}}{e}^{+})$ at tree level. In our setup an electron $A$ scatters with a positron $B$, which is initially entangled with another electron $C$ (spectator), that does not participate directly to the process. We find that the QED scattering generates and distributes entanglement in a nontrivial way among the three particles; the correlations in the output channels $AB$, $AC$, and $BC$ are studied in detail as functions of the scattering parameters and of the initial entanglement weight. Although derived in a specific case, our results exhibit some general features of other similar QED scattering processes, for which the extension of the present analysis is straightforward.

Physical review. D/Physical review. D.May 16, 202420 citations

A

scatters with a positron

B

, which is initially entangled with another electron

C

(spectator), that does not participate directly to the process. We find that the QED scattering generates and distributes entanglement in a nontrivial way among the three particles; the correlations in the output channels

AB

AC

, and

BC

are studied in detail as functions of the scattering parameters and of the initial entanglement weight. Although derived in a specific case, our results exhibit some general features of other similar QED scattering processes, for which the extension of the present analysis is straightforward.