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.
We review recent progress in understanding quantum entanglement generated by
2→2 scattering processes in quantum field theory. Starting from the final-state density matrix, we discuss two complementary approaches to quantifying entanglement: projection onto fixed final-state momenta and tracing out the momentum degrees of freedom. We present analytic results for the concurrence of a mixed two-qubit final state and identify the role of quantum coherences, showing that the real part of the inelastic forward scattering amplitude constitutes a subleading correction to the linearized entropy connected to the relative entropy of coherence. Our framework is illustrated through two phenomenologically relevant examples: high-energy scattering of two flavored scalars in the two-Higgs doublet model and high-energy electron-positron annihilation in QED.
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→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.
A bstract We regard the weak isospin of the Higgs doublet as a qubit and classify the entanglement measures for the Higgs scattering in the Standard Model Effective Field Theories (SMEFT) and their Ultra-Violet complete models. We consider Higgs scattering in the unbroken phase of electroweak symmetry. Treating the final state as a momentum-isospin bipartite system, we obtain von Neumann and linear entropies to quantify momentum-isospin correlation. From the momentum reduced state, we calculate the concurrence, which measures the entanglement between the two isospins. Both quantities are set by the isospin singlet and triplet scattering amplitudes, and hence by the Wilson coefficients of the dimension-6 and dimension-8 Higgs operators. We find that the von Neumann entropy grows as a function of the total energy in SMEFT as compared to the SM case, but it undergoes a cancellation in the medium energy below the cut-off scale due to the interference effects between the dimension-4 and dimension-8 operators, in particular, when the effective interactions stem dominantly from a massive graviton. Assuming the dominance of dimension-8 operators, we find the conditions for entanglement suppression/generation in the forward or backward scatterings or across all the kinematics. We also show the correlations between the entanglement suppression and the positivity bounds in the forward limit.
We construct the entanglement entropy of a general scattering process between one particle species (denoted as
A) and the rest of the final state. Assuming a pure initial momentum eigenstate, we show that the reduced density matrix in particle
A's Fock space is block-diagonal in zero-, one- and multi-particle states, and is diagonal in the momentum basis for the one-particle state. As a result, we could write down the Von Neumann entropy of particle
A,
SA, in terms of scattering probabilities and differential cross sections, assuming no more than one particle
A is produced in the final state.
SA contains the information of both the total scattering probabilities (or cross sections) and the differential distributions --- the latter depends on a phase-space resolution factor as a result of the infinite-dimensional momentum Hilbert space. Our result is general and model-independent since we consider the full final state from time evolution (
S∣i⟩) rather than a specific outcome, and is applicable as long as the probability for producing multiple particle
A is subleading. We also obtain the
n≥2 Tsallis and Rényi entropies in our framework and find out that, at the leading order, they are proportional to the total scattering probability and carry no differential information.
We are interested in the entanglement entropy of the final state of two particles in an elastic scattering. One can expect that the entanglement is yielded by the interaction between the particles. Within an S-matrix theory, by using the partial wave expansion of the S-matrix elements for two-particle states, we calculate a density matrix in a high energy elastic scattering, and obtain the entanglement entropy formula, which is described by physical observables. In the derivation of this formula, there appear divergences due to the infinite volume of two-particle Hilbert space. In order to avoid such divergences, we suggest a volume-regularization. Then we concretely evaluate the entanglement entropy for proton-proton scattering by using experimental data.