In an accelerator, two Higgs particles collide. For a fleeting moment, their fates intertwine, then separate, carrying away information about the encounter. A physicist would usually describe this with diagrams and amplitudes, but here the scattering is viewed as a quantum computation: each particle is a qubit, and the collision is an operation that transforms the quantum state.
Quantum magic as an invisible conductor tuning the symphony of symmetries. Magic is a resource that gives a quantum computer an advantage over a classical one. If a state is "magical," it cannot be efficiently simulated on an ordinary computer. In the new work, the magic of Higgs particles in scattering turns out to be conserved: the initial and final states contain the same amount of magic. This requirement, expressed through the commutator of the transition matrix and the density matrix, imposes strict constraints on possible interactions. In the first order of perturbation theory in quark couplings, the scattering amplitude becomes proportional to the identity matrix in flavor space, leading to a potential with maximal SO(8) symmetry.
Previously, it was unclear whether a single quantum-information principle could explain the emergence of symmetries in the Higgs sector for all scattering channels. Now it is shown that conservation of magic in two-particle scattering leads to SO(8) symmetry of the potential in the general case, and to SU(2)_R symmetry for states with definite isospin. This is achieved by treating scattering as a quantum operation on flavor and isospin qubits and requiring the transition matrix to commute with the density matrix of the initial state. Practically, this approach can serve as a guide for constructing extensions of the Standard Model with natural alignment, for example, for dark matter models.
Taking into account Bose statistics and the presence of isospin, the picture becomes more subtle. For an arbitrary initial state, the condition of magic conservation again singles out the SO(8)-symmetric potential, but for states with definite isospin (triplet states), only SU(2)_R symmetry in flavor space emerges. This is related to entanglement between flavor and isospin: when isospin is fixed, part of the magic is "locked" in entanglement, and the conductor allows less freedom. Singlet states impose no constraints at all.
Thus, quantum information becomes the architect of fundamental interactions. Instead of postulating symmetries, we can derive them from deeper conservation principles. The invisible conductor continues to tune the symphony, and now its score is clearer to read.
Magic states are a resource for quantum computing 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 a 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 information principles echoes 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.