We investigate the properties of quantum electrodynamics (QED) two-particle scattering processes when an arbitrarily sharp filtering of the outgoing particles in momentum space is performed. We find that these processes are described by dynamical quantum maps, whose structure is such that any initial state is transformed into a maximally entangled state, after an infinite number of iterations of the map. This structural property is exactly realized if all the colliding particles are massive fermions while, when photons are involved, it is verified in a partial way, depending on the process under consideration.
We study entanglement dynamics among helicity degrees of freedom in quantum electrodynamics (QED) scattering processes. For generic initial states, we consider scattering at fixed momentum, corresponding to a generalized measurement described by a positive operator-valued measure, resulting in a post-measurement state. Such processes are modeled in terms of quantum maps, whose spectral structure fully determines the associated entanglement dynamics. For scattering involving fermions only, maximal entanglement present in the initial state is always preserved. Moreover, iterating the corresponding quantum maps on arbitrary initial states, we obtain the fixed points of the maps, which, in the largest number of cases, are asymptotic (pure) maximally entangled states. The structure of the maps also accounts for the entanglement dynamics in processes involving both fermions and photons. The defining properties of these maps originate from discrete symmetries of the QED interaction.
We reformulate the phenomenon of maximal entanglement conservation in Quantum Electrodynamics (QED) scattering processes, previously discussed in earlier works, using the tools of quantum maps and invariant sets. These sets are characterized as hypersurfaces within the six-dimensional parameter space. Furthermore, we speculate over a possible irreversible (ever-increasing) behavior of entanglement in QED scatterings. • Complete transfer of maximal entanglement in Bhabha scattering. • QED scattering processes preserve maximal entanglement for fermionic systems. • We present the invariant sets representing the conserved maximally entangled states. • Preliminary studies suggest a global rise in entanglement in QED interactions. • Future work will address mixed states and all particle d.o.f.
We exploit the complete complementarity relations (CCR) to fully characterize various aspects of quantumness in quantum electrodynamics (QED) scattering processes at tree level. As a paradigmatic example, we consider Bhabha scattering in two different configurations: in the first case, the initial state is factorized in the spin and we study the generation of entanglement due to the scattering. Then we consider the most general case in which the initial state can be entangled: we find that the scattering generates and distributes quantum information in a nontrivial way among the spin degrees of freedom of the particles, with CCR relations being preserved. An important outcome of our analysis is that maximal entanglement is conserved in the scattering process involving only fermions as input and output states, with a more complex situation if photons are present.
We report on a systematic study on the entanglement between helicity degrees of freedom generated at tree level in quantum electrodynamics two-particle scattering processes. We determine the necessary and sufficient dynamical conditions for outgoing particles to be entangled with one another, and expose the hitherto unknown generation of maximal or nearly maximal entanglement through Bhabha and Compton scattering. Our work is an early step in revisiting quantum field theory and high-energy physics in the light of quantum information theory.
We consider a general quantum field relativistic scattering involving two half-spin fermions,
A and
B, which are initially entangled with another fermion
C that does not participate in the scattering dynamics. We construct general expressions for the reduced spin matrices for the out-state considering a general tripartite spin-entangled state. In particular we study an inelastic QED process at tree-level, namely ${e}^{\ensuremath{-}}{e}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}$ and a half-spin fermion
C as a spectator particle which can be entangled to the
AB system in the following ways: W state, GHZ state, $|{\mathrm{A}}^{\ensuremath{\alpha}}⟩\ensuremath{\bigotimes}|{\mathrm{\ensuremath{\Psi}}}^{\ifmmode\pm\else\textpm\fi{}}{⟩}_{\mathrm{BC}}$, and $|{\mathrm{A}}^{\ensuremath{\alpha}}⟩\ensuremath{\bigotimes}|{\mathrm{\ensuremath{\Phi}}}^{\ifmmode\pm\else\textpm\fi{}}{⟩}_{\mathrm{BC}}$, where ${|{\mathrm{\ensuremath{\Psi}}}^{\ifmmode\pm\else\textpm\fi{}}⟩,|{\mathrm{\ensuremath{\Phi}}}^{\ifmmode\pm\else\textpm\fi{}}⟩}$ are the Bell basis states and $|{\mathrm{A}}^{\ensuremath{\alpha}}⟩$ is a spin superposition state of system
A. We calculate the von Neumann entropy variation before and after the scattering for the particle
C and show that spin measurements in
C contain numerical information about the total cross section of the process. We compare the initial states W and GHZ as well as study the role played by the parameter $\ensuremath{\alpha}$ in the evaluation of the entropy variations and the cross section encoded in the spectator particle.
We study the behavior of entanglement between different degrees of freedom of scattering fermions, based on an exemplary QED scattering process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. The variation of entanglement entropy between two fermions from an initial state to the final state was computed, with respect to different entanglement between the ingoing particles. This variation of entanglement entropy is found to be proportional to an area quantity, the total cross section. We also study the spin-momentum and helicity-momentum entanglements within one particle in the aforementioned scattering process. The calculations of the relevant variations of mutual information in the same inertial frame reveals that, for a maximally entangled initial state, the scattering between the particles does not affect the degree of both of these entanglements of one particle in the final state. It is also found that the increasing degree of entanglement between two ingoing particles would restrict the generation of entanglement between spin (helicity) and momentum of one outgoing particle. And the entanglement between spin and momentum within one particle in the final state is shown to always be stronger than that for helicity-momentum for a general initial entanglement state, implying significantly distinct properties of entanglement for the helicity and spin perceived by an inertial observer.