A Study of the Entanglement's Entropy Variation in Elastic Scattering Processes for a 4 Complex Model

Abstract

This thesis aims to evaluate the legitimacy of the role attributed to an elastic scattering procedure as an hypothetical "Entanglement (creation and enhancement) Machine" (EceM). We study such a collision in the framework of Q.F.T (Quantum Field Theory), where the interaction is given by the coupling between two scalar elds, Alice's (A) and Bob's (B) with a 4 interaction. Using the Von Neumann entropy as a measure of entanglement, which we call the "Entropy of Entanglement" (SE), we calculate (SE)in from a state of momenta before the collision ("in-state") and (SE)out from the state of momenta after the collision ("out-state") to determine, ( SE) (SE)out (SE)in: Thus, we can determine the entanglement between subsystems A and B in the degrees of freedom of momentum before and after the states "enter" the EceM and judge how well the collision behaves as one, knowing that ( SE) > 0 is the condition that must be met. We separate the calculation into two distinct case studies: -When the "in-state" is separable; -When the "in-state" already has some degree of entanglement; As such we can analyse if the scattering procedure behaves di erently when it has to create entanglement from scratch or enhance the already existing one. ( SE) is shown to have an explicit dependence on the velocities of the CM (center of momentum) frame which corresponds to the momenta of the initial state, and on the coupling of the interaction ( ). These variables could be interpreted as "parameters" of the machine, which we can regulate to create the best possible con guration. We analyse the collision diagrammatically, computing up to 1-loop contributions when the "in-state" is separable. Thus, we can compare how this changes the "performance" of the machine, and how the parameters for the best possible outcome vary.