The Standard Model of particle physics is based on gauge symmetries, but their specific form is not derived from first principles; it is determined experimentally. Finding mechanisms that generate symmetry is a long-standing problem in theoretical physics. Recent work has shown that minimizing entanglement in particle scattering can lead to the emergence of symmetries, for example in the two-Higgs-doublet model (2HDM). However, results for different scattering channels are contradictory: in some cases symmetry appears, in others it does not. This work continues that direction, using a stronger principle, conservation of non-stabilizerness, or 'magic', and extends the analysis to all two-particle scattering channels, taking into account Bose statistics and isospin invariance. This places the work among studies where quantum information serves as a tool for understanding the structure of fundamental interactions.
The authors consider 2→2 scattering in a simplified 2HDM, where the flavor of each Higgs doublet is treated as a qubit, and weak isospin as an additional qubit degree of freedom. The initial state is given by a product of states in momentum, flavor, and isospin spaces, and due to particle identity it is Bose-symmetrized. The transition matrix T is computed to first order in perturbation theory in the quartic couplings. The key condition is commutativity [T, ρ₀] = 0, where ρ₀ is the density matrix of the initial state. This condition is equivalent to conservation of the linearized stabilizer entropy (a measure of magic) to first order. The authors compute the magic of the initial and final states and require their equality, which leads to constraints on the scattering amplitudes and hence on the parameters of the potential.
For the channel Φ⁺Φ⁰ → Φ⁺Φ⁰, the condition of magic conservation leads to the amplitude matrix being proportional to the identity: $M_{ijkl}$ = M $δ_{ik}$ $δ_{jl}$. This imposes the relations λ₁ = λ₂ = λ₃/2 ≡ λ and zeroes the other quartic couplings, generating the maximally symmetric potential V₄ = λ(Φ₁†Φ₁ + Φ₂†Φ₂)². This potential has SO(8) symmetry and automatically realizes the alignment limit, in which one of the Higgs bosons resembles the Standard Model Higgs boson. When extending to all two-particle channels and including isospin as a qubit, for an arbitrary initial state SO(8) symmetry emerges again. However, for states with definite isospin (triplet states), the commutativity condition gives only SU(2)_R symmetry in flavor space, corresponding to a potential invariant under global rotations of the doublets. For singlet states, no constraints arise. The antisymmetric momentum wavefunction adds no new conditions.
The work shows that magic conservation is a stronger condition than entanglement minimization, and it can single out unique symmetric structures of the potential. Unlike previous studies, where symmetry appeared only in certain channels, here a unified principle is proposed that covers all two-particle processes. Taking into account Bose statistics and isospin reveals the subtle role of entanglement between flavor and isospin: it is precisely this entanglement that leads to the reduction from SO(8) to SU(2)_R for states with definite isospin. This deepens the understanding of the connection between quantum information and symmetries in quantum field theory and offers a new tool for building models beyond the Standard Model, where symmetries are not postulated but derived.
A natural next step is to go beyond first-order perturbation theory and include many-particle states. This will require a more careful scattering formalism and will allow testing whether the connection between magic and symmetry persists at a deeper level. It is also important to consider channels with total particle number P=0, which are omitted here. Including interactions with gauge bosons and fermions will pave the way to realistic phenomenological models, such as the inert two-doublet model or the left-right symmetric model. In addition, it is interesting to explore what other quantum-information measures, besides magic and entanglement, can serve as generators of symmetries.
The results may influence the construction of extensions of the Standard Model, especially in the context of dark matter and the naturalness problem. The proposed principle can be applied to other theories where symmetries arise dynamically.
Test the magic conservation condition at higher orders in perturbation theory and for channels with P=0. Include interactions with gauge fields and fermions to study phenomenological consequences.
In particle physics, the origin of gauge symmetries and the mass hierarchy remains an open question. This work links the emergence of symmetry to quantum-information constraints, which may shed light on the naturalness problem and the structure of the Higgs sector. In particular, natural alignment in the 2HDM, usually requiring fine-tuning, here emerges as a consequence of magic conservation, which is a new approach to a long-standing problem.
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What the work does
The authors study 2→2 scattering in the two-Higgs-doublet model, treating flavor and isospin as qubits. They require the preservation of non-stabilizerness (magic) under collisions, which is equivalent to the commutativity of the transition matrix with the density matrix of the initial state. This condition leads to a maximal SO(8) symmetry of the quark potential for arbitrary states and to an SU(2)_R symmetry for isospin triplets.
Where its strength is
A strong point is the use of a stricter condition (preservation of magic, not just entanglement), which yields unambiguous constraints on the potential parameters and links quantum information to the emergence of symmetry.
Where it could go next
Worth trying
Why this may matter
If the principle of magic conservation turns out to be universal, it could provide a new way to derive symmetries from quantum information requirements, potentially useful for building models beyond the Standard Model.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.56, against a usual 0.64. It looks like few have drilled nearby.
Magic states are a resource for quantum computation that cannot be efficiently simulated on a classical computer. In this work, the magic of Higgs particles in scattering turns out to be 'conserved', leading to symmetry of the potential. Interestingly, the term 'magic' in quantum information was introduced by analogy with magic states that allow bypassing the limitations of the Gottesman-Knill theorem.
The idea that fundamental symmetries of nature might arise from informational principles resonates with the concept of 'digital physics' in science fiction, for example in Greg Egan's novel 'Permutation City', where reality is modeled as a computational process. However, in this work the connection to fiction is more conceptual than direct.