Maximal Entanglement in Higgs Boson Scattering Doubles the Symmetry ✦
We study 2→2 scattering of Higgs bosons in the CP-conserving two-Higgs-doublet model (2HDM) in the context of maximizing quantum entanglement in flavor space, where the two doublets Φ₁ and Φ₂ are treated as basis states of a qubit. Scattering amplitudes are computed and the condition of maximal entanglement of final states in the computational basis is imposed. In the unbroken phase without gauge interactions, this condition leads to a global U(2)×U(2) symmetry for the quartic couplings, softly broken by mass terms. When vacuum expectation values appear, maximal entanglement requires an exact U(2)×U(2) symmetry, which is spontaneously broken down to U(1)×U(1), generating Higgs alignment and six massless Nambu-Goldstone bosons. Gauging this symmetry allows the removal of Goldstone bosons, but maximal entanglement then becomes possible only with a discrete Z₂ symmetry swapping the two gauge sectors. The scalar sector possesses custodial invariance, and adding fermions requires a mirror dark sector linked to the Standard Model by the same Z₂ symmetry.
Context
Understanding the origin of symmetries is one of the key unsolved problems in modern physics. Typically, symmetries such as the gauge symmetry of the Standard Model are introduced as postulates, but could they arise from deeper principles, for instance, from requirements of quantum information? The theorem of Emmy Noether links symmetries to conservation laws, yet it does not explain their origin. Recent studies have revealed an intriguing correlation between the suppression of quantum entanglement and the emergence of symmetries. In this work, this idea is developed using the two-Higgs-doublet model Higgs boson (2HDM), where the flavor states of the two doublets can be treated as qubits—the basic elements of quantum information, the study of which began with pioneering work by Erwin Schrödinger. Requiring that the scattering of these 'qubits' always produces maximally entangled states unexpectedly leads to a doubling of symmetry and predicts a dark sector, which could shed light on the nature of dark matter.
Methods
The work employed the mathematical apparatus of quantum field theory to compute the 2→2 scattering amplitudes of Higgs bosons within the CP-conserving 2HDM. The flavor states of the two doublets were represented in the computational basis {|00⟩, |01⟩, |10⟩, |11⟩}, with each doublet acting as a qubit. To quantify entanglement, entropic measures (concurrence) related to von Neumann entropy were used. The maximal entanglement condition was imposed for all initial states from this basis and for all kinematic channels, requiring the exact matching of flavor structures of contact, s-, t-, and u-channel diagrams. The analysis was performed both in the unbroken phase with global U(2) symmetry and after spontaneous electroweak symmetry breaking, where the contribution of the Higgs vacuum expectation value (v ≈ 246 GeV) was taken into account. Additionally, the influence of gauge fields and loop corrections was examined to verify the robustness of the result.
Results
Main result: maximal entanglement in all channels is achieved only for a specific relation among the quartic coupling constants: λ₁ = λ₂ = λ₃ = λ₄ = ±λ₅, and λ₆ = λ₇ = 0. In the unbroken phase, this generates a global U(2)×U(2) symmetry among the scalar interactions, although mass terms softly break it. However, after acquiring vacuum expectation values, the requirement of maximal entanglement forces the mass terms to also respect this symmetry, making it exact. Consequently, the symmetry U(2)×U(2) is spontaneously broken to U(1)×U(1), leading to six massless Goldstone bosons (matching the number of broken generators) and two degenerate massive scalars. An important phenomenological consequence is automatic Higgs alignment: the 125 GeV Higgs boson, predicted by Peter Higgs, possesses the standard couplings to W and Z bosons without fine-tuning, in agreement with LHC experiments.
Implications
This discovery points to a deep connection between quantum information principles and the structure of physical theories. Maximal entanglement acts as an organizing principle that dictates symmetries and the particle spectrum, much like entropy drives ordering in statistical physics. These results could be a step toward a program of deriving fundamental interactions from informational postulates, potentially explaining why the Standard Model has this particular set of symmetries. Moreover, the maximal entanglement condition requires the existence of a mirror dark sector, providing new motivation for dark matter searches.
Future development
In the future, this approach could be generalized to more complex gauge theories, including grand unified theories. It would be interesting to study the behavior of maximal entanglement conditions in a cosmological context, for example, in the early Universe where exotic symmetries might have existed. It is also important to investigate whether maximal entanglement in particle scattering could be experimentally detected at future colliders, which would open up a new direction of 'entropic phenomenology'. Possibly, the connection to quantum error-correcting codes could allow methods of quantum computing to be applied to simulate such processes.
Impact
The work impacts particle physics, quantum field theory, and quantum information. It suggests that the search for a dark sector may be motivated by information principles, not only by astrophysical observations.
Next steps
Next steps include a detailed study of the phenomenology of the mirror dark sector, including possible signals at colliders and in cosmic rays, as well as the development of methods for experimentally testing maximal entanglement in scattering.
Key open problems
The results are directly connected to the problem of the origin of symmetries in nature and the mass hierarchy. The discovered link to a quantum repetition code (quantum error correction) hints that fundamental physics may use mechanisms similar to quantum information protection to stabilize symmetries.
🎯 Interestingly, the requirement of maximal entanglement is actually equivalent to post-selection in a quantum repetition code: the system automatically discards states that are not invariant under a discrete Z₂ symmetry—as if nature 'programs' symmetries at the quantum level.
🎬 The idea of a mirror world where every particle has a dark twin resonates with the concept of a 'Mirror Universe' from science fiction, for instance, in the series Star Trek or in Isaac Asimov's novel The Gods Themselves, where parallel universes interact through fundamental forces.
Key numbers
- Electroweak scale: 246 GeV
- Number of massless Goldstone bosons: 6
- Higgs boson mass: 125 GeV
- Number of degenerate massive scalars: 2
- Coupling constant ratio: ±1