Pith. sign in

REVIEW 3 major objections 4 minor 7 cited by

Emergent symmetry in a two-Higgs-doublet model from quantum information and nonstabiliserness

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Forcing 2-to-2 scalar scattering to conserve quantum magic restricts the two-Higgs-doublet quartic potential to a maximally symmetric SO(8) form, or to an SU(2)_R-symmetric form for definite-isospin states.

desk verdict An interesting extension of the emergent-symmetry idea to magic conservation, but the load-bearing equivalence between magic conservation and [T, ρ0] = 0 is asserted rather than shown. read the letter →

arxiv 2506.01314 v2 pith:O54MNBO3 submitted 2025-06-02 hep-ph hep-thquant-ph

Giorgio Busoni , John Gargalionis , Ewan N. V. Wallace , Martin J. White This is my paper
classification hep-phhep-thquant-ph PACS 03.67.-a11.30.-j12.60.Fr
keywords two-Higgs-doubletmodelnonstabilisernessmagicemergentsymmetrySO(8)SU(2)_Ralignmentlimitscatteringamplitudes
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper's thesis is that one quantum-information conservation law can generate the symmetries model builders normally impose by hand on the two-Higgs-doublet scalar potential. The law is conservation of nonstabiliserness, or 'magic,' in 2-to-2 scalar scattering, which the authors show is equivalent at leading order to demanding that the initial-state density matrix commute with the transition matrix. Applied to all two-particle scattering channels, that commutator condition forces the quartic potential to the maximally symmetric SO(8) form $V_4 = \lambda(\Phi_1^\dagger\Phi_1 + \Phi_2^\dagger\Phi_2)^2$ when the initial state is arbitrary, and to the smaller SU(2)$_R$-symmetric form with $\lambda_1 = \lambda_2 = (\lambda_3 + \lambda_4)/2$ and $\lambda_5 = \lambda_6 = \lambda_7 = 0$ when the initial state has definite weak isospin. Both constrained forms automatically satisfy the alignment limit, so if the argument is correct a single information-theoretic principle explains why the observed Higgs boson is Standard Model-like without fine-tuning. A careful reader would care because the same highly symmetric potentials that model builders impose ad hoc are here derived from a conservation law.

What carries the argument

The carrying object is the linearised stabiliser entropy $M_{\mathrm{lin}}(\rho) = 1 - (1/2^n)\sum_P \mathrm{Tr}^4(\rho P)$, a faithful measure of nonstabiliserness (magic) defined by summing over products of Pauli matrices; a state has zero magic exactly when it is a stabiliser state, the class efficiently simulable by Clifford circuits. The argument's load-bearing identity is that demanding $M_{\mathrm{lin}}(\rho_f) = M_{\mathrm{lin}}(\rho_0)$ to first order in the quartic couplings is equivalent to $[T, \rho_0] = 0$, because any nonvanishing commutator would change the magic at $O(\lambda)$. The Hilbert space is partitioned as $\mathcal{H}_2 \simeq \mathcal{H}_p \otimes \mathcal{H}_{\mathrm{iso}} \otimes \mathcal{H}_{\mathrm{flav}}$, giving four qubits (two for isospin, two for flavour), and the $T$-matrix is written in blocks built from singlet and triplet bilinears of SU(2)$_L \otimes$ SU(2)$_R$; Bose symmetry fixes which combinations of those blocks can appear in $\rho_0$. The commutator then acts as a linear constraint on the quartic parameters, and requiring it to vanish for all allowed initial states forces the $T$-blocks to be proportional to the identity, which translates directly into the quoted relations among $\lambda_1,\dots,\lambda_7$.

What would settle it

Exhibiting a single Bose-symmetric two-particle initial state for which the transition matrix and the initial state commute, but the quartic couplings are not $\lambda_1 = \lambda_2 = (\lambda_3 + \lambda_4)/2$ with $\lambda_5 = \lambda_6 = \lambda_7 = 0$, would falsify the definite-isospin derivation, because the paper's algebra says no such state exists. A complementary check is to compute the linearised stabiliser entropy to second order in the quartic couplings for a definite-isospin triplet initial state: if magic is not conserved at that order for the SU(2)$_R$-symmetric potential, the leading-order principle fails to extend in the way stated.

Watch

Extended reading notes

Core claim

The central claim is that magic conservation is not just a bookkeeping device: it is a symmetry-generating constraint. At leading order in the quartic couplings, requiring the linearised stabiliser entropy of the final state to match the initial state is exactly the condition $[T, \rho_0] = 0$, where $T$ is the transition matrix and $\rho_0$ the initial two-particle density matrix. Writing the two doublets as a bidoublet under SU(2)$_L \otimes$ SU(2)$_R$ and representing each scattering channel as a four-qubit system (two isospin qubits, two flavour qubits), the authors decompose the $T$-matrix into singlet and triplet blocks. Bose symmetry restricts the initial-state density matrix and entangles the isospin and flavour sectors. For an arbitrary allowed initial state, the commutator vanishes only if both blocks are proportional to the identity on the relevant subspaces, which fixes $\lambda_1 = \lambda_2 = \lambda_3/2$ and all other quartic couplings to zero, recovering the maximally symmetric SO(8) potential. For a definite-isospin triplet initial state, the singlet block drops out and the condition only forces the triplet block to be proportional to the identity, giving $\lambda_1 = \lambda_2 = (\lambda_3 + \lambda_4)/2$ and $\lambda_5 = \lambda_6 = \lambda_7 = 0$, the SU(2)$_R$-symmetric potential; scattering a singlet or using an antisymmetric momentum wave function imposes no further constraints. In both constrained cases the potential satisfies the alignment condition, so a Standard Model-like Higgs can emerge without a tuned parameter.

Load-bearing premise

The whole derivation rests on two linked assumptions: that at leading order the momenta of the two scattered particles remain unentangled with their flavour and isospin quantum numbers, so the two-particle state stays effectively pure, and that magic conservation for every allowed initial state really is equivalent to the strong condition that the transition matrix and the initial density matrix commute; if either assumption fails, the forced SO(8) and SU(2)_R conclusions do not follow.

Editorial extensions

If this is right

  • Magic conservation is strictly stronger than entanglement minimisation: it forces the transition matrix to be proportional to the identity gate for an arbitrary initial state, whereas the entanglement conditions allow single-qubit operations.
  • For an arbitrary two-particle initial state, the quartic potential is forced to the maximally symmetric SO(8) form, which realises the alignment limit with no fine-tuning.
  • For a definite-isospin triplet initial state, the emergent symmetry is the smaller SU(2)$_R$ with $\lambda_1 = \lambda_2 = (\lambda_3 + \lambda_4)/2$ and $\lambda_5 = \lambda_6 = \lambda_7 = 0$, and this also satisfies the alignment condition.
  • Because the commutator vanishes, the final and initial density matrices agree to order $\lambda^2$, so every information measure built from the density matrix, not just magic, is conserved at leading order.
  • Singlet initial states and antisymmetric momentum wave functions impose no further constraints on the quartic couplings, so the symmetry selection is driven entirely by the triplet scattering channels.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper leaves the quadratic, gauge, and fermion sectors unconstrained; a natural extension is to test whether the same commutator condition, applied after electroweak symmetry breaking, selects the full potential rather than only its quartic part.
  • Because the definite-isospin result singles out the same SU(2)$_R$-symmetric quartic as a left-right symmetric scalar bidoublet, one testable extension is to run the two-particle magic-conservation analysis in a left-right symmetric model and see whether it reproduces the bidoublet potential without extra assumptions.
  • If the principle is meant to survive coupling to the rest of the Standard Model, the arbitrary-state result, which forces the transition matrix to the identity gate, is a stress test: future embeddings will need to specify which initial states count as allowed, since all mathematically conceivable two-particle states may be too broad a set.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes that leading-order 2→2 scalar scattering in a two-Higgs-doublet model conserves nonstabiliserness (magic), formulates this as commutativity [T, rho0] = 0, and shows that this condition restricts the quartic potential. For Phi+ Phi0 scattering in flavour space it obtains M_{ijkl} = M delta_{ik} delta_{jl}, which forces the maximally symmetric SO(8) potential lambda (Phi1^dagger Phi1 + Phi2^dagger Phi2)^2 and hence natural alignment. Extending the Hilbert space by an explicit isospin qubit and imposing Bose symmetry, the paper finds that scattering an arbitrary two-particle initial state again forces the SO(8) form, while scattering a definite-isospin triplet state forces an SU(2)_R symmetric form with lambda1 = lambda2 = (lambda3 + lambda4)/2 (and, properly, lambda5 = lambda6 = lambda7 = 0). An antisymmetric momentum wave function is shown to impose no constraints.

Significance. If the missing derivation is supplied, this is a worthwhile contribution: it shows that a single information-theoretic principle, rather than hand-picked symmetries, selects the highly symmetric quartic potentials that realize the alignment limit, and it clarifies the relation between magic conservation and previously studied entanglement minimisation (Eq. (15) is a special case of Eq. (17)). The paper is not circular: the lambda_i are outputs, the mapping Eq. (27) is explicit and checkable, and the role of Bose symmetry in entangling isospin and flavour is clearly identified. The main limitation is that the advertised equivalence between magic conservation and [T, rho0] = 0 is asserted rather than demonstrated; until that step is shown, the emergent-symmetry results are conditional on an additional postulate.

major comments (3)
  1. [Sec. III, Eq. (15)] The derivation of Eq. (15) is the load-bearing step of the paper, but it is not shown. The text states that expanding the final-state linearised stabiliser entropy to first order and demanding that the resulting polynomial in B_{ij}, B*_{ij} vanish identically 'results in' M_{ijkl} = M delta_{ik} delta_{jl}. This is a nontrivial implication: the first-order variation of M_lin is a single scalar polynomial in the state coefficients, while Eq. (15) is a matrix identity on the four-qubit amplitude. Equation (16) establishes only that Eq. (15) implies [T, rho0] = 0 and hence magic conservation; the converse direction, which is needed to justify using [T, rho0] = 0 as the guiding principle in Secs. III and IV, is asserted. Please display the full expansion of Delta M_lin and prove that identical vanishing in B_{ij} forces Eq. (15), or state the commutator condition as an independent postulate and adjust the claims accordingly.
  2. [Sec. IV C, Eqs. (27) and (40)] The commutation condition for the isospin-triplet initial state is said to enforce lambda_T proportional to 1_3. Reading this through Eq. (27), that condition requires not only lambda1 = lambda2 = (lambda3 + lambda4)/2 but also lambda5 = lambda6 = lambda7 = 0. The displayed Eq. (40) omits the vanishing of the off-diagonal entries; a potential obeying only Eq. (40) is not invariant under the SU(2)_R flavour rotation and, for generic beta_{1,n}, does not satisfy [T, rho0] = 0. The statement of the emergent SU(2)_R result should be corrected to the full set of conditions, and the same point should be made explicit in the abstract and conclusions if they quote the shortened form.
  3. [Sec. II C] The paper assumes that the flavour and momentum degrees of freedom remain unentangled at leading order, so that the final-state flavour density matrix is rho_f = rho0 + i[T, rho0] and Tr(rho_f^2) = 1 + O(lambda^2). This is stated with a pointer to Ref. [9] but not demonstrated in this manuscript. The pure-state definition of M_lin in Eq. (4) is then applied to rho_f; if the partial trace over momentum produces O(lambda^2) corrections, a discussion of why they do not affect the O(lambda) variation of M_lin would make the derivation self-contained. Since this assumption underlies the expansion used to obtain Eq. (15), please either prove it from the leading-order contact interactions or state it explicitly as an assumption.
minor comments (4)
  1. [Eq. (9)] The momentum-state normalisation appears to be missing the usual factors; it should presumably read (2 pi)^6 4 E_{p1} E_{p2} delta^{(3)}(p1 - q1) delta^{(3)}(p2 - q2).
  2. [Sec. II A] The phrase 'vanishing entanglement power' in the Introduction is used without definition; please add a definition or a precise citation.
  3. [Secs. III--IV] The same symbol rho is used for the full two-particle density matrix, the reduced flavour-space density matrix, and the isospin-flavour density matrix after Bose symmetrisation; please distinguish these objects notationally to avoid confusion.
  4. [Sec. IV C] The notation lambda_T ~ 1_3 should be defined explicitly; as written it is unclear whether it means proportional to the 3x3 identity matrix or merely equal diagonal entries.

Circularity Check

0 steps flagged · score 2.0 of 10

No load-bearing circularity: the quartic couplings are outputs of an algebraic commutator condition, not fitted inputs; the only self-citations are contextual.

full rationale

The derivation chain is not circular. The quartic couplings lambda_i enter only as components of the T-matrix and are solved from <ij|[T,rho0]|kl>=0 for generic (or definite-isospin) initial states in Secs. III and IV, so they are outputs, not fitted inputs. The paper explicitly states that the resulting amplitude condition M_ijkl = M delta_ik delta_jl is a special case of the existing entanglement-minimisation conditions (Eq. (17)); this is a logical implication, not a renaming of a known result, and the new content is the claimed equivalence with magic conservation plus the SU(2)_R extension for definite-isospin states. The main caveat is a derivational gap rather than circularity: the equivalence between first-order conservation of the linearised stabiliser entropy and [T,rho0]=0 is asserted in Sec. III ('This results in the following condition...'; 'it is straightforward to verify...') without the intermediate algebra. If that equivalence is weaker than full commutativity, the central claim would fail, but that would be a correctness problem, not a reduction of the output to the input by construction. The only self-citations (Refs. [14,18], both involving author M. J. White) are used for contextual review of magic formalism and top-pair magic applications; neither supplies the symmetry conditions, so they are not load-bearing. Accordingly, the circularity score is low.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The paper introduces no fitted free parameters and no invented physical entities. The seven quartic couplings are inputs of the two-Higgs-doublet model, constrained by the principle rather than fitted to data. The central postulate is the commutativity condition [T, rho0] = 0, classified as ad hoc to this paper because no deeper mechanism is supplied. The remaining axioms are standard quantum field theory and quantum-information background plus stated modelling simplifications, including CP conservation, leading-order flavour-momentum separability, and Bose-symmetrised initial states.

assumptions (6)
  • domain assumption The flavour and isospin degrees of freedom remain unentangled with momentum at leading order in the quartic couplings, so that rho_f = rho0 + i[T, rho0] + O(lambda^2) and the final state is pure to first order.
    Invoked in Sec. II C, Eq. (14), with a citation to Ref. [9]; the paper does not prove the separation in the text.
  • domain assumption Explicit CP conservation with real quartic couplings and a U(1)_EM invariant minimum, so that the alignment condition of Eq. (6) applies.
    Stated in Sec. II B; the alignment-limit conclusions presuppose these simplifications.
  • ad hoc to paper The guiding principle that leading-order 2-to-2 scattering conserves magic, which the paper shows is equivalent to [T, rho0] = 0.
    This is the main postulate; it is not derived from the Lagrangian or from external data, and the paper notes it is equivalent to conservation of any measure when the commutator vanishes.
  • domain assumption Bose symmetry of the two identical scalar particles is imposed by taking the product of isospin, flavour and momentum wavefunctions to be symmetric or antisymmetric under particle exchange.
    Used in Sec. IV A to obtain Eq. (30) and the correlated structure of the initial density matrix.
  • domain assumption At leading order, the quartic potential is the sole source of 2-to-2 scattering, and the bilinear mass terms do not enter the amplitudes.
    Used in the T-matrix of Eq. (19) and in the general construction of Sec. IV A.
  • standard math SU(2) Clebsch-Gordan decomposition of the bidoublet bilinear into singlet and triplet pieces under SU(2)_L and SU(2)_R.
    Eqs. (22)-(27); the rewriting of the potential and the T-matrix relies on this standard group theory.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Emergent symmetry in a two-Higgs-doublet model from quantum information and nonstabiliserness." pith.science (2026). https://pith.science/paper/O54MNBO3

@misc{pith2026250601314,
  author       = {Pith},
  title        = {Pith review of: Emergent symmetry in a two-Higgs-doublet model from quantum information and nonstabiliserness},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O54MNBO3}},
  note         = {Machine review of arXiv:2506.01314}
}
abstract

Studies of scattering processes in scalar models with two Higgs doublets have recently hinted at a connection between the absence of flavour-space entanglement in $\Phi^+\Phi^0$ scattering and an emergent $\mathrm{SO}(8)$ 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 flavour subspaces of the $2$-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 minimisation conditions previously derived in the literature, and we interpret the principle in terms of the conservation of non-stabiliserness (or magic). Working at leading order in the quartic couplings, we find a consistent set of conditions that implies an $\mathrm{SO}(8)$ symmetry on the quartic part of the potential for scattering an arbitrary initial state, but a smaller $\mathrm{SU}(2)_R$ 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 flavour subspaces.

Discussion (0). Sign in to comment.

Forward citations

Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Magic without a phase: phase-independent stabilizer R\'enyi entropy in gluon scattering

    hep-th 2026-07 conditional novelty 7.0 of 10

    A phase-averaged stabilizer Rényi entropy is introduced for tree-level gluon scattering, with color-independent phase-independent magic that is larger in 3→2 than 2→2 and has a soft-limit lower bound in 2→3.

  2. High Energy Photon Polarimetry at Lepton Colliders: Quantum Information from Converted Photons

    hep-ph 2026-07 conditional novelty 6.5 of 10

    Converted photons in Belle II enable high-significance measurements of Bell nonlocality, discord, concurrence, magic and steerability for macroscopically separated GeV diphotons, provided opening-angle resolution reac...

  3. Systematic analysis of 3HDM symmetries

    hep-ph 2025-12 conditional novelty 6.0 of 10

    A systematic catalogue of realisable Higgs-family, general-CP, and GOOFy/T-GOOFy symmetries in three-Higgs-doublet models, with new invariant potentials and a corrected U(1)◦V4 group structure.

  4. Parameter Inference from Final-State Entanglement in Higgs Decays

    hep-ph 2025-11 conditional novelty 6.0 of 10

    With a spin/color-weighted entanglement entropy built from Higgs branching ratios, the Standard Model Higgs and W masses sit near the global maximum, and the preferred coupling ratio is SM-like.

  5. Entanglement, Yang-Mills, and the Scattering Matrix as an SU(N)-equivariant Kernel

    hep-ph 2025-11 conditional novelty 6.0 of 10

    SU(N) symmetry fixes the entangling power of 2→2 scattering: Yang-Mills adjoint scattering has a group-only entanglement maximum at 90° (3/4 for SU(2), ≈0.91 for SU(3)), and maximal-entanglement preservation selects t...

  6. Spin versus Magic: Lessons from Gluon and Graviton Scattering

    hep-th 2025-08 accept novelty 6.0 of 10

    For 2 to 2 scattering of massless spin-1/2 to spin-2 particles, the averaged generated magic decreases monotonically with spin, with maxima well below the two-qubit upper bound.

  7. Gedanken Experiments of Entanglement in Particle Physics: Interactions, Operators and Bell Inequalities in Flavor Space

    hep-ph 2025-12 conditional novelty 4.0 of 10

    Mass-identification, kaon-decay, and weak-mixing observables can be cast as spin-like operators whose correlations violate a Bell-type bound (0.44+0.90=1.34>1) in an idealized Gedanken framework.

Reference graph

Works this paper leans on

30 extracted references · 6 canonical work pages · cited by 7 Pith papers

  1. [9]

    Carena, I

    M. Carena, I. Low, C. E. M. Wagner, and M.-L. Xiao, Phys. Rev. D 109, L051901 (2024), arXiv:2307.08112 [hep-ph]

    arXiv 2024

  2. [1]

    = 1 by con- struction, so the initial state is pure; and it may further be shown that Tr( ρ2 f ) = 1 + O(λ2), so the final state is also pure (to first order in perturbation theory). III. MAGIC CONSER V A TION AND THE ALIGNMENT LIMIT We now commence our investigation of conservation of magic and emergent symmetry by computing the magic for the initial and...

    work page

  3. [2]

    Essential to this result is the fact that the initial state is a superposition of states of differing total isospin, as seen clearly in Eq

    In this particular case, the commutator reduces to 1 2 " λS 0 0 ( λT )n,n′δm,m′ , |β0,0|2 δ0,m′β0,0β∗ 1,n′ δ0,mβ1,nβ∗ 0,0 δ0,mδ0,m′β1,nβ∗ 1,n′ # (38) but for arbitrary β0,0, β1,n, it remains true that the only circumstance in which this object can vanish is that de- scribed above, recovering the maximal symmetry. Essential to this result is the fact that ...

    work page

  4. [3]

    McGinnis, (2025), arXiv:2504.21079 [hep-th]

    N. McGinnis, (2025), arXiv:2504.21079 [hep-th]

    arXiv 2025

  5. [4]

    S. R. Beane, D. B. Kaplan, N. Klco, and M. J. Savage, Phys. Rev. Lett. 122, 102001 (2019), arXiv:1812.03138 [nucl-th]

    arXiv 2019

  6. [5]

    Low and T

    I. Low and T. Mehen, Phys. Rev. D 104, 074014 (2021), arXiv:2104.10835 [hep-th]

    arXiv 2021

  7. [6]

    Q. Liu, I. Low, and T. Mehen, Phys. Rev. C 107, 025204 (2023), arXiv:2210.12085 [quant-ph]

    arXiv 2023

  8. [7]

    Liu and I

    Q. Liu and I. Low, Phys. Lett. B 856, 138899 (2024), arXiv:2312.02289 [hep-ph]

    arXiv 2024

Show all 30 references
  1. [8]

    Thaler and S

    J. Thaler and S. Trifinopoulos, Phys. Rev. D 111, 056021 (2025), arXiv:2410.23343 [hep-ph]

    2025 arXiv

  2. [10]

    Chang and G

    S. Chang and G. Jacobo, Phys. Rev. D 110, 096020 (2024), arXiv:2409.13030 [hep-ph]. 9

    2024 arXiv

  3. [11]

    Kowalska and E

    K. Kowalska and E. M. Sessolo, JHEP 07, 156 (2024), arXiv:2404.13743 [hep-ph]

    2024 arXiv

  4. [12]

    Carena, G

    M. Carena, G. Coloretti, W. Liu, M. Littmann, I. Low, and C. E. M. Wagner, (2025), arXiv:2505.00873 [hep-ph]

    2025 arXiv

  5. [13]

    Cervera-Lierta, J

    A. Cervera-Lierta, J. I. Latorre, J. Rojo, and L. Rottoli, SciPost Phys. 3, 036 (2017), arXiv:1703.02989 [hep-th]

    2017 arXiv

  6. [14]

    N´ u˜ nez, A

    C. N´ u˜ nez, A. Cervera-Lierta, and J. I. Latorre, (2025), arXiv:2504.15353 [hep-th]

    2025

  7. [15]

    Zanardi, C

    P. Zanardi, C. Zalka, and L. Faoro, Phys. Rev. A 62, 030301 (2000), arXiv:quant-ph/0005031

    2000 arXiv

  8. [16]

    C. D. White and M. J. White, Phys. Rev. D 110, 116016 (2024), arXiv:2406.07321 [hep-ph]

    2024 arXiv

  9. [17]

    Quan- tum Magic and Computational Complexity in the Neu- trino Sector,

    I. Chernyshev, C. E. P. Robin, and M. J. Savage, “Quan- tum Magic and Computational Complexity in the Neu- trino Sector,” (2024), arXiv:2411.04203 [quant-ph]

    2024 arXiv

  10. [18]

    Quantum Magic in Quan- tum Electrodynamics,

    Q. Liu, I. Low, and Z. Yin, “Quantum Magic in Quan- tum Electrodynamics,” (2025), arXiv:2503.03098 [quant- ph]

    2025 arXiv

  11. [19]

    CMS Collaboration, Observation of magic states of top quark pairs produced in proton-proton collisions at√s = 13 TeV, Tech. Rep. (CERN, Geneva, 2025)

    2025

  12. [20]

    Aoude, H

    R. Aoude, H. Banks, C. D. White, and M. J. White, (2025), arXiv:2505.12522 [hep-ph]

    2025 arXiv

  13. [21]

    C. D. White, C. Cao, and B. Swingle, Phys. Rev. B 103, 075145 (2021), arXiv:2007.01303 [quant-ph]

    2021 arXiv

  14. [22]

    Garc ´ ıa, I

    H. Garc ´ ıa, I. Markov, and A. Cross, Quantum Informa- tion and Computation 14, 683 (2014)

    2014

  15. [23]

    Gottesman, in 22nd International Colloquium on Group Theoretical Methods in Physics(1998) pp

    D. Gottesman, in 22nd International Colloquium on Group Theoretical Methods in Physics(1998) pp. 32–43, arXiv:quant-ph/9807006

    1998 arXiv

  16. [24]

    Leone, S

    L. Leone, S. F. E. Oliviero, and A. Hamma, Phys. Rev. Lett. 128, 050402 (2022), arXiv:2106.12587 [quant-ph]

    2022 arXiv

  17. [25]

    Wang and Y

    Y. Wang and Y. Li, Quant. Inf. Proc. 22, 444 (2023)

    2023

  18. [26]

    P. S. Bhupal Dev and A. Pilaftsis, JHEP 12, 024 (2014), [Erratum: JHEP 11, 147 (2015)], arXiv:1408.3405 [hep- ph]

    2014 arXiv

  19. [27]

    Darvishi, M

    N. Darvishi, M. R. Masouminia, and A. Pilaftsis, Phys. Rev. D 104, 115017 (2021), arXiv:2106.03159 [hep-ph]

    2021 arXiv

  20. [28]

    Darvishi and A

    N. Darvishi and A. Pilaftsis, Phys. Rev. D 101, 095008 (2020), arXiv:1912.00887 [hep-ph]

    2020 arXiv

  21. [29]

    S. Seki, I. Y. Park, and S.-J. Sin, Phys. Lett. B 743, 147 (2015), arXiv:1412.7894 [hep-th]

    2015 arXiv

  22. [30]

    Darvishi, A

    N. Darvishi, A. Pilaftsis, and J.-H. Yu, JHEP 05, 233 (2024), arXiv:2312.00882 [hep-ph]

    2024 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.