Studies of scattering processes in scalar models with two Higgs doublets have recently hinted at a connection between the absence of flavor-space entanglement in Φ + Φ 0 scattering and an emergent SO(8) symmetry in the scalar potential. We extend the analysis to all scattering channels with two particles in the external states by treating the process as a four-qubit system in the weak isospin and flavor subspaces of the two-particle state. We work with a generic quantum-information-theoretic principle encoded by the commutativity of the initial-state density matrix with the transition matrix (at leading order in perturbation theory). This yields a special case of the entanglement minimization conditions previously derived in the literature, and we interpret the principle in terms of the conservation of nonstabilizerness (or “magic”). Working at leading order in the quartic couplings, we find a consistent set of conditions that implies an SO(8) symmetry on the quartic part of the potential for scattering an arbitrary initial state but a smaller SU ( 2 ) R symmetry when the initial state is chosen to have definite isospin. This follows by accounting for Bose symmetry in the initial state, which introduces entanglement between the isospin and flavor subspaces.
Studies of scattering processes in scalar models with two Higgs doublets have recently hinted at a connection between the absence of flavor-space entanglement in Φ + Φ 0 scattering and an emergent SO(8) symmetry in the scalar potential. We extend the analysis to all scattering channels with two particles in the external states by treating the process as a four-qubit system in the weak isospin and flavor subspaces of the two-particle state. We work with a generic quantum-information-theoretic principle encoded by the commutativity of the initial-state density matrix with the transition matrix (at leading order in perturbation theory). This yields a special case of the entanglement minimization conditions previously derived in the literature, and we interpret the principle in terms of the conservation of nonstabilizerness (or “magic”). Working at leading order in the quartic couplings, we find a consistent set of conditions that implies an SO(8) symmetry on the quartic part of the potential for scattering an arbitrary initial state but a smaller SU ( 2 ) R symmetry when the initial state is chosen to have definite isospin. This follows by accounting for Bose symmetry in the initial state, which introduces entanglement between the isospin and flavor subspaces.
In this paper, we study a recently discovered connection between scattering that minimally entangles and emergent symmetries. In a perturbative expansion, we have generalized the constraints of minimal entanglement scattering, beyond qubits, to general qudits of dimension d . Interestingly, projecting on any qubit subspaces, the constraints factorize, so that it is consistent to analyze minimal entanglement by looking at all such subspaces. We start by looking at toy models with two scalar fields, finding that minimal entanglement only allows quartic couplings which have instabilities at large field values and no symmetries. For the two Higgs doublet model, by considering H + H − → H + H − scattering, we show that minimal entanglement in this channel does not allow an interacting parameter point with enhanced symmetries. These results show that the connection between minimal entanglement and symmetries depends strongly on the scattering channels analyzed and we speculate on the potential resolutions. Published by the American Physical Society 2024
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 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.
Abstract Quantum entanglement provides a quantitative measure of nonclassical correlations and plays a central role in quantum information theory. Identifying and quantifying the mechanisms by which fundamental interactions generate or suppress entanglement is therefore of conceptual interest. In this work, flavor entanglement generated in pion–pion scattering is analyzed within a post-selected framework, in which the outgoing two-pion state is conditioned on fixed asymptotic momenta. The analysis is carried out in the isospin-symmetric limit using chiral perturbation theory, including one-loop corrections to the scattering amplitude. A general formalism is developed to quantify post-selected flavor entanglement through the von Neumann entropy of the reduced flavor density matrix, expressed in terms of a flavor tensor characterizing the initial state. This framework is applied to initially unentangled charged two-pion states. Except for the ∣++⟩ | + + ⟩ and ∣−−⟩ | - - ⟩ channels, which remain unentangled due to isospin conservation, the post-selected final states exhibit nontrivial flavor entanglement and behave effectively as entangled qubits or qutrits. The entanglement is maximal near threshold and typically peaks at scattering angles close to θ=π/2 θ = π / 2 . The analysis demonstrates that isospin-channel dominance plays a central role in shaping the entanglement structure: the I=0 I = 0 channel drives generic initial states toward highly entangled qutrit configurations after scattering and post-selection. Conversely, suitably chosen initial superpositions can undergo a reduction of entanglement, showing that the strong interaction can act both as a generator and a suppressor of quantum correlations. One-loop corrections quantitatively redistribute entanglement across phase space, sharpening angular structures that appear more diffuse at tree level.
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.