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Journal of Physics A Mathematical and Theoretical

Perturbative approach to entanglement generation in QFT using the S matrix

Ricardo Faleiro, R. Pavao, H. A. S. Costa, Brigitte Hiller, Alex H. Blin, Marcos Sampaio

Published Jul 2, 2020• 11 citations
Publisher

Abstract

Abstract We compute the variation of the von Neumann (VN) entropy Δ S between the asymptotic in and out momenta modes of a real scalar field A, when elastically scattered against the modes of another scalar field B. This is done to see how the entanglement between the two fields’ momenta changes under the scattering procedure. The calculation is separated into two case studies, one where the fields’ asymptotic in states are separable, and another where they are arbitrarily entangled. We perform a perturbative calculation to one loop order in the separable case, and verify that Δ S changes in a non-trivial way when we vary the momentum of the incoming field modes and/or the coupling of the theory. Finally, also in the separable case, we show an explicit dependence between Δ S and the cross-section of the collision, consistent with perturbation theory.

DOI
10.1088/1751-8121/aba214

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Abstract We compute the variation of the von Neumann (VN) entropy Δ S between the asymptotic in and out momenta modes of a real scalar field A, when elastically scattered against the modes of another scalar field B. This is done to see how the entanglement between the two fields’ momenta changes under the scattering procedure. The calculation is separated into two case studies, one where the fields’ asymptotic in states are separable, and another where they are arbitrarily entangled. We perform a perturbative calculation to one loop order in the separable case, and verify that Δ S changes in a non-trivial way when we vary the momentum of the incoming field modes and/or the coupling of the theory. Finally, also in the separable case, we show an explicit dependence between Δ S and the cross-section of the collision, consistent with perturbation theory.
We compute the entanglement entropy variation between initial (separable or entangled in the momenta) and final states ΔSEΔS_EΔSE​ in an elastic scattering of a bipartite system composed by two interacting scalar particles. We perform a quantum field theoretical calculation to one loop order and verify that $ΔS_E $ changes as we vary the energy of incoming particles and the coupling strength in a non-trivial way.
Understanding the dependence of entanglement entropy on the renormalized mass in quantum field theories can provide insight into phenomena such as quantum phase transitions, since the mass varies in a singular way near the transition. Here we perturbatively calculate the entanglement entropy in interacting scalar field theory, focusing on the dependence on the field’s mass. We study λϕ 4 and g ϕ 3 theories in their ground state. By tracing over a half space, using the replica trick and position space Green’s functions on the cone, we show that spacetime volume divergences cancel and renormalization can be consistently performed in this conical geometry. We establish finite contributions to the entanglement entropy up to two-loop order, involving a finite area law. The resulting entropy is simple and intuitive: the free theory result in d = 3 (that we included in an earlier publication) Δ S ∼ A m 2 ln ( m 2 ) is altered, to leading order, by replacing the bare mass m by the renormalized mass m r evaluated at the renormalization scale of zero momentum.
A bstract We investigate quantum entanglement in high-energy 2 → 2 scalar scattering, where the scalars are characterized by an internal flavor quantum number acting like a qubit. Working at the 1-loop order in perturbation theory, we build the final-state density matrix as a function of the scattering amplitudes connecting the initial to the outgoing state. In this construction, the unitarity of the S -matrix is guaranteed at the required order by the optical theorem. We consider the post-scattering entanglement between the momentum and flavor degrees of freedom of the final-state particles, as well as the entanglement of the two-qubit flavor subsystem. In each case we identify the couplings of the scalar potential that can generate, destroy, or transfer entanglement between different bipartite subspaces of the Hilbert space.
We investigate quantum entanglement in high-energy 2→22\to 22→2 scalar scattering, where the scalars are characterized by an internal flavor quantum number acting like a qubit. Working at the 1-loop order in perturbation theory, we build the final-state density matrix as a function of the scattering amplitudes connecting the initial to the outgoing state. In this construction, the unitarity of the SSS-matrix is guaranteed at the required order by the optical theorem. We consider the post-scattering entanglement between the momentum and flavor degrees of freedom of the final-state particles, as well as the entanglement of the two-qubit flavor subsystem. In each case we identify the couplings of the scalar potential that can generate, destroy, or transfer entanglement between different bipartite subspaces of the Hilbert space.
A bstract In the context of entanglement in relativistic 2 → 2 scattering described by a perturbative S -matrix, we derive analytically the concurrence for a mixed final state of two qubits corresponding to a discrete quantum number of the scattered particles. The qubit density matrix is obtained by tracing the momentum degrees of freedom out of the full density matrix of the scattered system. Given an initial product state, the derived concurrence depends at the leading order on the real part of the inelastic forward amplitude and the initial state only. We also point out that the real part of the forward amplitude provides a subleading correction to the linearized entropy, reducing it by an amount that, for a computational-basis state, is equivalent to the relative entropy of coherence. We illustrate our findings with two examples of phenomenological interest: high-energy scattering of two scalar fields in the two-Higgs doublet model, and high-energy electron-positron annihilation.