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Physical review. D/Physical review. D.

Entanglement distribution in Bhabha scattering with an entangled spectator particle

Massimo Blasone A, Gaetano Lambiase, Bruno Micciola

Published May 16, 2024• 20 citations
Publisher

Abstract

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.

DOI
10.1103/physrevd.109.096022

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We analyze how entanglement is generated and distributed in a Bhabha scattering process (e\ensuremath−e+\ensuremath→e\ensuremath−e+)({e}^{\ensuremath{-}}{e}^{+}\ensuremath{\rightarrow}{e}^{\ensuremath{-}}{e}^{+})(e\ensuremath−e+\ensuremath→e\ensuremath−e+) at tree level. In our setup an electron AAA scatters with a positron BBB, which is initially entangled with another electron CCC (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 ABABAB, ACACAC, and BCBCBC 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−e+→e−e+)(e^-e^+\rightarrow e^-e^+)(e−e+→e−e+) at tree level. In our setup an electron AAA scatters with a positron BBB, which is initially entangled with another electron CCC (spectator), that does not participate directly to the process. We find that the QED scattering generates and distributes entanglement in a non-trivial way among the three particles: the correlations in the output channels ABABAB, ACACAC and BCBCBC 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.
From the perspective of quantum information science, we investigate tree-level Bhabha scattering between an incident electron AAA and a positron BBB, where BBB is initially entangled with a spectator electron CCC, which does not participate in the scattering interaction. We find that the quantum electrodynamics (QED) scattering between AAA and BBB can drive the global ABCABCABC system into a genuine tripartite entangled (GTE) state. Using four canonical tripartite entanglement metrics, we systematically characterize and quantify the GTE of the composite system, and demonstrate that the scattering momentum of the AAA-BBB pair and the initial BBB-CCC entanglement are the key resources governing GTE generation. We further analyze the monogamy of quantum correlations, which imposes fundamental constraints on the shareability of quantum resources in multipartite systems. Specifically, we systematically study the monogamy relations for the squared entanglement of formation and squared quantum discord in our scattering model, and find that monogamy constraints are markedly relaxed in the non-relativistic regime, enabling enhanced shareability of quantum correlations across the three particles. This work uncovers novel quantum correlation properties of fundamental QED scattering processes, and provides direct theoretical guidance for the development of QED-based quantum information processing protocols.
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 consider a general quantum field relativistic scattering involving two half-spin fermions, AAA and BBB, which are initially entangled with another fermion CCC 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 CCC as a spectator particle which can be entangled to the ABABAB 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 AAA. We calculate the von Neumann entropy variation before and after the scattering for the particle CCC and show that spin measurements in CCC 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 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 investigate spin-outcome correlations and memory-assisted entropic uncertainty in tree-level Bhabha scattering, where an incident electron AAA scatters with a positron BBB initially entangled with a spectator electron CCC. For the fixed-angle post-selected final state, we compare the total memory-assisted uncertainty UAU_AUA​ for three alternative Pauli measurements on AAA with the entanglement entropy S(ρA)S(ρ_A)S(ρA​) across the A∣BCA|BCA∣BC partition. We resolve UAU_AUA​ into the separate uncertainties UBU_BUB​ and UCU_CUC​ and evaluate the corresponding outcome-memory mutual-information sums GBG_BGB​ and GCG_CGC​. This separates changes in the randomness of the outcomes on AAA from changes in their correlations with each memory. In the parameter regions studied, enhanced A∣BCA|BCA∣BC entanglement is accompanied by lower UAU_AUA​, most prominently near high-energy backscattering. An analytic treatment of this limit shows that BBB factorizes from ACACAC: GBG_BGB​ vanishes, whereas GCG_CGC​ increases with the initial BBB-CCC entanglement. An entropic complete complementarity analysis characterizes the accompanying loss of local helicity predictability in ρAρ_AρA​ and changes in the coherence, predictability, and mixedness of the interacting pair ρABρ_{AB}ρAB​. These results show that initial BBB-CCC entanglement can lower the total memory-assisted uncertainty in high-energy backscattering by strengthening spin-outcome correlations with the spectator CCC, thereby identifying the distinct roles of the interacting particle and the spectator as quantum memories.