Pith. sign in

REVIEW 3 major objections 4 minor 98 references

This paper defines a phase-independent stabilizer Rényi entropy and shows that in tree-level gluon scattering the resulting magic depends only on kinematics, with 3→2 final states reaching ln(27/13) ≈ 0.731.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-02 06:07 UTC pith:J7DBMNPS

load-bearing objection The phase-averaged construction is real and the gluon calculations are clean, but fM2 is not a monotone (H on |+> takes it from 0 to ln(8/7)), so the 'magic measure' framing is unsupported as it stands. the 3 major comments →

arxiv 2607.13134 v1 pith:J7DBMNPS submitted 2026-07-14 hep-th hep-phquant-ph

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

Jinwei Chu , Savan Kharel This is my paper
classification hep-th hep-phquant-ph
keywords stabilizer Rényi entropynon-stabilizernessmagic statesgluon scatteringhelicity amplitudesphase-independent magicParke–Taylor amplitudesquantum information in scattering
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Magic, the resource that lets quantum states escape efficient classical simulation, is usually measured relative to a chosen computational basis, and a local phase change of that basis continuously changes the measured value. The paper's central move is to define a phase-independent stabilizer Rényi entropy, fMq, by averaging the Pauli-expectation sum over all U(1)^k phase redefinitions before the logarithm, making it invariant under the one ambiguity that helicity data leave unresolved. The paper applies this to tree-level gluon scattering, where each gluon's two helicities serve as one qubit, and finds that the color dependence cancels: the phase-independent magic is fixed by kinematics alone. In 3→2 scattering the invariant never vanishes and reaches ln(27/13) ≈ 0.731, higher than anything 2→2 can attain; in 2→3 scattering it is confined between a soft-limit floor of ln(8/7) ≈ 0.134 and a ceiling near 0.38, with the symmetric outgoing configuration only a few percent above the floor. A sympathetic reader should care because this yields a way to ask whether a scattering process is classically simulable without needing to know phase conventions that the physics does not fix.

Core claim

The core claim is that the phase ambiguity inherent in helicity data can be quotiented out of the stabilizer Rényi entropy, producing a new invariant, fMq, and that for tree-level gluon amplitudes this invariant is a simple function of helicity moduli. For 2→2 scattering with incoming helicities |+−⟩, fM2 depends only on the scattering angle, vanishes at forward/backward angles, and peaks at ln(7/5) ≈ 0.34. For 3→2 scattering with incoming |++−⟩, the same invariant never vanishes and attains ln(27/13) ≈ 0.731, so the three-to-two process is guaranteed to carry nonzero magic and beats the best two-to-two value. For 2→3 scattering, the first three-qubit case, fM2 is bounded below by ln(8/7) ≈

What carries the argument

The central object is the phase-independent stabilizer Rényi entropy fMq (Eq. 3.13), defined by averaging the Pauli-string sum inside the logarithm over the U(1)^k orbit of local phase redefinitions of the qubit basis — a 'typical-phase' rather than minimized invariant. Its work is to remove the basis-phase ambiguity from magic so that the result depends only on the moduli of the helicity-amplitude coefficients. The machinery that makes the gluon application tractable is the Parke–Taylor form of maximally helicity-violating (MHV) and anti-MHV amplitudes together with the identity |⟨ij⟩| = |[ij]|, which forces the color-kinematic sums S and S̄ to have equal moduli, so all color factors drop o

Load-bearing premise

The load-bearing premise is that fMq behaves as a genuine magic resource measure even though the paper does not establish its monotonicity, and — separately — that the asserted 2→3 formula (Eq. 5.20) is correct, since every 2→3 result depends on it.

What would settle it

Directly average the second SRE over the full U(1)^3 phase orbit for the 2→3 final state and compare with Eq. (5.20): any disagreement would falsify the formula. Alternatively, exhibit a quantum operation built from Clifford gates and stabilizer measurements that strictly increases fMq on some state, which would show the phase-averaged quantity is not a resource monotone and would undercut the interpretation of the numbers as a conserved quantum-computational resource.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • 2→2 gluon scattering with initial |+−⟩: fM2 is a function of the scattering angle alone, vanishing at θ=0 and θ=π and peaking at ln(7/5) ≈ 0.34, with a residual local minimum ln(8/7) ≈ 0.134 at θ=π/2.
  • 3→2 scattering with symmetric incoming momenta and initial |++−⟩: fM2 never vanishes and reaches ln(27/13) ≈ 0.731 when the outgoing momenta are perpendicular to the incoming plane, exceeding every 2→2 value.
  • 2→3 scattering with initial |++⟩: fM2 is bounded, with soft-limit floor ln(8/7) ≈ 0.134 and ceiling ≈ 0.38; the symmetric three-outgoing-momenta configuration sits at a local minimum only a few percent above the floor.
  • In all computed cases the color dependence cancels from the phase-averaged quantity, so fM2 is entirely determined by helicity-amplitude moduli — kinematics alone.
  • Since the integrated phases are exactly what a polarization measurement leaves unresolved, fM2 is the invariant to use when discussing magic from amplitudes whose phase frame is not physically fixed.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If fMq turns out not to be a resource monotone, the numbers in this paper remain well-defined kinematic invariants of the amplitude; the 'magic as resource' reading would then need a separate proof or a modified measure, such as a minimized phase orbit.
  • The color cancellation likely reflects a structural fact about MHV/anti-MHV amplitudes: phase averaging leaves only coefficient moduli, and those moduli factor into color-independent ratios whenever the amplitudes share a single Parke–Taylor sum; this suggests the cancellation will persist at higher multiplicity within the same helicity sector, which can be checked directly.
  • The near-flatness of fM2 near the symmetric 2→3 configuration suggests a kind of kinematic saturability: the invariant may be locally insensitive to momentum variations around symmetric points, a property that could be tested by computing its gradient in momentum space.
  • One testable extension is to carry the same phase-averaging prescription to graviton or fermion scattering, where the double-copy and spin structures change the coefficient moduli; the paper's framing implies each amplitude sector will acquire its own phase-independent magic function.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The manuscript defines a phase-independent variant of the stabilizer Rényi entropy, fM_q, by moving the U(1)^k phase average inside the logarithm in the Pauli-sum expression (Eq. 3.13). It derives closed two-qubit formulas (Eqs. 3.9, 3.17) and applies them to tree-level gluon scattering, interpreting helicities as qubits. The reported results are: 2→2 scattering gives fM2 between 0 and ln(7/5); 3→2 scattering with initial helicity |++−⟩ reaches fM2 = ln(27/13) ≈ 0.731; 2→3 scattering has a soft-limit floor ln(8/7) ≈ 0.134 and a symmetric-limit value ≈ 0.140. The paper also shows that, for the MHV/anti-MHV configurations considered, the color dependence cancels in the ratios of coefficient moduli and hence in fM2. Section 6 explicitly leaves open whether fM_q is a resource monotone.

Significance. If the interpretation can be made rigorous, the paper offers a concrete, basis-phase-robust quantum-information observable for scattering amplitudes, and the color-cancellation result is a clean and checkable fact. The use of exact Parke–Taylor amplitudes, the explicit analytic formulas for the two-qubit cases, and the identification of the soft-limit and symmetric-limit values are strengths. However, the central resource-theoretic status is unresolved: for the standard stabilizer free operations, fM2 is demonstrably not a monotone, and the three-qubit formula (5.20) is asserted without derivation. The numerical results may survive as phase-invariant kinematic quantities, but the advertised notion of a 'phase-independent magic' resource is not yet supported.

major comments (3)
  1. [Section 6, Eq. (3.13)] The paper leaves open whether fM_q is a resource monotone. For fM2 this is not merely open: it is false under the standard stabilizer free operations. For |ψ⟩ = |+⟩, phase redefinitions change the state only by an overall phase, so fM2 = 0. Applying the Clifford H gives H|+⟩ = (|+⟩ + |−⟩)/√2; for this state the phase-redefined Pauli expectations are 1, cos θ, sin θ, 0, and averaging (3.13) yields −ln(7/8) = ln(8/7), precisely the value quoted as the 2→3 soft-limit floor (5.27). Thus a free Clifford operation strictly increases fM2. The kinematic numbers may survive as well-defined invariants, but the 'phase-independent magic' resource interpretation requires either a monotonicity proof for a suitably restricted class of phase-covariant free operations, or an explicit reframing of fM_q as a phase-invariant quantifier rather than a resource measure.
  2. [Section 5.3, Eq. (5.20)] All of the 2→3 results rest on the three-qubit formula (5.20), but it is introduced with only 'One can calculate using (3.13)' and no derivation is provided. This is load-bearing: the soft-limit floor (5.27), the symmetric-limit value (5.28), and the behavior in Fig. 8 all follow from this formula. Please supply the averaging calculation in the text or in an appendix. If the formula is correct, the section can stand; without a derivation, the 2→3 conclusions are unsupported.
  3. [Section 3, Eqs. (3.5) and (3.13)] The paper first defines \bar M_q (3.5) as the true average of M_q over the U(1)^k phases, then says the integral is hard, introduces the average-inside-the-log expression (3.8), and finally proposes (3.13) as the 'phase-independent SRE.' These are different quantities: Jensen's inequality gives fM_q ≤ \bar M_q, not equality. The manuscript should state unambiguously that fM_q, not \bar M_q, is the proposed measure, and that (3.5) is only motivation. As written, the transition around (3.5)–(3.8) and Figure 3 can be read as if the two quantities were interchangeable, which is misleading for the central definition.
minor comments (4)
  1. [Eq. (5.11)] The coefficient E should presumably involve \bar S rather than S; the subsequent ratio (5.13) and the color-cancellation argument depend on this. Please correct the typo.
  2. [Eq. (4.9) and text after (5.12)] The sign convention for spinor products should be made consistent: the paper writes ⟨jl⟩ = [lj]^* in (4.9) but later uses ⟨ij⟩ = −[ij]^*. If these are different conventions, the difference should be stated explicitly.
  3. [Introduction / Section 5.2] The phrase 'far beyond anything 2→2 can reach' should be qualified as 'the maximum attained in the analyzed 2→2 family': the global two-qubit SRE maximum in Eq. (2.10) is ln(16/7) ≈ 0.827, which is larger than ln(27/13) ≈ 0.731. The statement is about the phase-independent quantity in the specific 2→2 channel.
  4. [References] Reference [71] (CMS 'Observation of magic states of top quark pairs...') is missing a journal reference or arXiv number; it should be completed before publication.

Circularity Check

0 steps flagged

No significant circularity: fMq is computed from the stated SRE definition and standard Parke-Taylor amplitudes, with no fitted parameters or load-bearing self-citations.

full rationale

The paper's central object fMq (Eq. 3.13) is an explicit phase-average of the stabilizer Rényi entropy; the two-qubit and three-qubit formulas (3.17) and (5.20) are direct evaluations of that definition, and the gluon coefficients (5.11) and (5.22) come from the color-dressed DDM decomposition with Parke-Taylor partial amplitudes. The color cancellation follows from |⟨ij⟩|=|[ij]| and the common factor S in (5.11), not from any fit. The toy model in Section 2 is motivational only: the paper explicitly computes the amplitudes for the 3→2 and 2→3 kinematics and does not tune the amplitudes to reproduce the toy values. There are no fitted parameters, no data subset, and no self-citations; the admitted open question of whether fMq is a resource monotone (Section 6) and the asserted-without-derivation formula (5.20) are correctness/completeness concerns, not circularity. The derivation chain is therefore self-contained: definition → exact Pauli sum → Parke-Taylor amplitudes → closed-form fM2. Score 0.

Axiom & Free-Parameter Ledger

0 free parameters · 5 axioms · 0 invented entities

The paper introduces no fitted parameters and no new physical entities. The load-bearing assumptions are prior resource-theory results, the helicity-as-qubit dictionary, the choice to average over U(1)^k phases inside the log, and the unshown 3-qubit Pauli-sum identity (5.20).

axioms (5)
  • domain assumption The stabilizer Rényi entropy M_q is a computable magic measure, and for q≥2 it is a resource monotone (Leone-Oliviero-Hamma; Haug-Piroli; Leone-Bittel).
    Invoked in §2 (Eq. 2.1) to justify using M2 as the magic measure.
  • domain assumption A color- and momentum-fixed tree-level helicity amplitude defines the polarization wavefunction of k outgoing gluons, i.e. a k-qubit state.
    Introduced in §4 (Eqs. 4.1-4.4); this dictionary is the basis for all gluon applications.
  • ad hoc to paper Averaging the Pauli sum over the U(1)^k phase orbit (Eq. 3.13) gives the correct phase-independent generalization of SRE.
    This is the paper's central construction; its operational meaning is not fully settled (min vs average; monotonicity open).
  • ad hoc to paper The phase-averaged Pauli sum for the four-coefficient 3-qubit state (5.19) equals 6(Σ|coef|^4)^2 −5Σ|coef|^8, Eq. (5.20).
    Stated in §5.3 as 'One can calculate' without derivation; it is load-bearing for the 2→3 results.
  • domain assumption Tree-level MHV/anti-MHV amplitudes are given exactly by the Parke-Taylor formula (4.8) and the DDM color decomposition (4.5).
    Used throughout §5 to compute the helicity coefficients.

pith-pipeline@v1.3.0-alltime-deepseek · 19949 in / 22270 out tokens · 201916 ms · 2026-08-02T06:07:04.810644+00:00 · methodology

0 comments
read the original abstract

Magic, also known as non-stabilizerness, measures the usefulness of a quantum state for quantum computation. While magic is defined relative to a choice of computational basis, in some physical settings the available data determine this basis only up to local phase conventions. In this paper, we generalize the notion of magic and formulate it in a phase-independent manner, and hence define a generalized stabilizer R\'enyi entropy. As a case study, we consider higher-multiplicity tree-level gluon scattering, interpreting the outgoing helicities as qubits. In this setting, the helicity data naturally determine a local basis for each qubit but leave a phase ambiguity. For $3\to 2$ scattering, we find that the final-state phase-independent magic is generically larger than the maximum attainable in $2\to 2$ scattering. For $2 \to 3$ scattering, we find a nonzero minimal value approached in the soft limit. Moreover, when the three outgoing momenta become symmetric, the magic approaches a local minimum only a few percent above the soft-limit value. In all cases considered, the color dependence cancels from the phase-independent stabilizer R\'enyi entropy.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

98 extracted references · 73 linked inside Pith

  1. [1]

    The Heisenberg representation of quantum computers,

    D. Gottesman, “The Heisenberg representation of quantum computers,” in22nd International Colloquium on Group Theoretical Methods in Physics, pp. 32–43. 7, 1998.arXiv:quant-ph/9807006

    Pith/arXiv arXiv 1998

  2. [2]

    Improved simulation of stabilizer circuits,

    S. Aaronson and D. Gottesman, “Improved simulation of stabilizer circuits,”Phys. Rev. A70no. 5, (2004) 052328,arXiv:quant-ph/0406196

    Pith/arXiv arXiv 2004

  3. [3]

    M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information. Cambridge University Press, 6, 2012

    2012

  4. [4]

    Universal quantum computation with ideal Clifford gates and noisy ancillas,

    S. Bravyi and A. Kitaev, “Universal quantum computation with ideal Clifford gates and noisy ancillas,”Phys. Rev. A71no. 2, (2005) 022316, arXiv:quant-ph/0403025

    Pith/arXiv arXiv 2005

  5. [5]

    The resource theory of stabilizer quantum computation,

    J. Emerson, D. Gottesman, S. A. H. Mousavian, and V. Veitch, “The resource theory of stabilizer quantum computation,”New J. Phys.16no. 1, (2014) 013009, arXiv:1307.7171 [quant-ph]

    Pith/arXiv arXiv 2014

  6. [6]

    Contextuality supplies the ‘magic’ for quantum computation,

    M. Howard, J. J. Wallman, V. Veitch, and J. Emerson, “Contextuality supplies the ‘magic’ for quantum computation,”Nature510no. 7505, (2014) 351–355, arXiv:1401.4174 [quant-ph]. – 21 –

    Pith/arXiv arXiv 2014

  7. [7]

    Lower bounds on the non-Clifford resources for quantum computations,

    M. Beverland, E. Campbell, M. Howard, and V. Kliuchnikov, “Lower bounds on the non-Clifford resources for quantum computations,”Quantum Sci. Technol.5no. 3, (2020) 035009,arXiv:1904.01124 [quant-ph]

    Pith/arXiv arXiv 2020

  8. [8]

    Stabilizer Rényi Entropy,

    L. Leone, S. F. E. Oliviero, and A. Hamma, “Stabilizer Rényi Entropy,”Phys. Rev. Lett.128no. 5, (2022) 050402,arXiv:2106.12587 [quant-ph]

    Pith/arXiv arXiv 2022

  9. [9]

    Stabilizer entropies and nonstabilizerness monotones,

    T. Haug and L. Piroli, “Stabilizer entropies and nonstabilizerness monotones,” Quantum7(2023) 1092,arXiv:2303.10152 [quant-ph]

    Pith/arXiv arXiv 2023

  10. [10]

    Stabilizer entropies are monotones for magic-state resource theory,

    L. Leone and L. Bittel, “Stabilizer entropies are monotones for magic-state resource theory,”Phys. Rev. A110no. 4, (2024) L040403,arXiv:2404.11652 [quant-ph]

    Pith/arXiv arXiv 2024

  11. [11]

    Pseudomagic Quantum States,

    A. Gu, L. Leone, S. Ghosh, J. Eisert, S. F. Yelin, and Y. Quek, “Pseudomagic Quantum States,”Phys. Rev. Lett.132no. 21, (2024) 210602,arXiv:2308.16228 [quant-ph]

    Pith/arXiv arXiv 2024

  12. [12]

    Magic-Induced Computational Separation in Entanglement Theory,

    A. Gu, S. F. E. Oliviero, and L. Leone, “Magic-Induced Computational Separation in Entanglement Theory,”PRX Quantum6no. 2, (2025) 020324,arXiv:2403.19610 [quant-ph]

    Pith/arXiv arXiv 2025

  13. [13]

    Scalable Measures of Magic Resource for Quantum Computers,

    T. Haug and M. S. Kim, “Scalable Measures of Magic Resource for Quantum Computers,”PRX Quantum4no. 1, (2023) 010301, arXiv:2204.10061 [quant-ph]

    Pith/arXiv arXiv 2023

  14. [14]

    Magic-state resource theory for the ground state of the transverse-field Ising model,

    S. F. E. Oliviero, L. Leone, and A. Hamma, “Magic-state resource theory for the ground state of the transverse-field Ising model,”Phys. Rev. A106no. 4, (2022) 042426,arXiv:2205.02247 [quant-ph]

    Pith/arXiv arXiv 2022

  15. [15]

    Quantifying nonstabilizerness of matrix product states,

    T. Haug and L. Piroli, “Quantifying nonstabilizerness of matrix product states,”Phys. Rev. B107no. 3, (2023) 035148,arXiv:2207.13076 [quant-ph]

    Pith/arXiv arXiv 2023

  16. [16]

    Complexity of frustration: A new source of non-local non-stabilizerness,

    J. Odavić, T. Haug, G. Torre, A. Hamma, F. Franchini, and S. M. Giampaolo, “Complexity of frustration: A new source of non-local non-stabilizerness,”SciPost Phys.15no. 4, (2023) 131,arXiv:2209.10541 [quant-ph]

    arXiv 2023

  17. [17]

    Nonstabilizerness via Perfect Pauli Sampling of Matrix Product States,

    G. Lami and M. Collura, “Nonstabilizerness via Perfect Pauli Sampling of Matrix Product States,”Phys. Rev. Lett.131no. 18, (2023) 180401,arXiv:2303.05536 [quant-ph]

    Pith/arXiv arXiv 2023

  18. [18]

    Efficient Quantum Algorithms for Stabilizer Entropies,

    T. Haug, S. Lee, and M. S. Kim, “Efficient Quantum Algorithms for Stabilizer Entropies,”Phys. Rev. Lett.132no. 24, (2024) 240602,arXiv:2305.19152 [quant-ph]

    Pith/arXiv arXiv 2024

  19. [19]

    Quantum State Designs with Clifford-Enhanced Matrix Product States,

    G. Lami, T. Haug, and J. De Nardis, “Quantum State Designs with Clifford-Enhanced Matrix Product States,”PRX Quantum6no. 1, (2025) 010345, arXiv:2404.18751 [quant-ph]

    Pith/arXiv arXiv 2025

  20. [20]

    Exact solution of long-range stabilizer Rényi entropy in the dual-unitary XXZ model∗,

    J. A. M. López and P. Kos, “Exact solution of long-range stabilizer Rényi entropy in the dual-unitary XXZ model∗,”J. Phys. A57no. 47, (2024) 475301, arXiv:2405.04448 [quant-ph]

    Pith/arXiv arXiv 2024

  21. [21]

    Magic Resources of the Heisenberg Picture,

    N. Dowling, P. Kos, and X. Turkeshi, “Magic Resources of the Heisenberg Picture,” Phys. Rev. Lett.135no. 5, (2025) 050401,arXiv:2408.16047 [quant-ph]. – 22 –

    Pith/arXiv arXiv 2025

  22. [22]

    Evaluating Many-Body Stabilizer Rényi Entropy by Sampling Reduced Pauli Strings: Singularities, Volume Law, and Nonlocal Magic,

    Y.-M. Ding, Z. Wang, and Z. Yan, “Evaluating Many-Body Stabilizer Rényi Entropy by Sampling Reduced Pauli Strings: Singularities, Volume Law, and Nonlocal Magic,” PRX Quantum6no. 3, (2025) 030328,arXiv:2501.12146 [quant-ph]

    Pith/arXiv arXiv 2025

  23. [23]

    Stabilizer entropy and entanglement complexity in the Sachdev-Ye-Kitaev model,

    B. Jasser, J. Odavić, and A. Hamma, “Stabilizer entropy and entanglement complexity in the Sachdev-Ye-Kitaev model,”Phys. Rev. B112no. 17, (2025) 174204,arXiv:2502.03093 [quant-ph]

    arXiv 2025

  24. [24]

    Non-stabilizerness of Sachdev-Ye-Kitaev model,

    S. Bera and M. Schirò, “Non-stabilizerness of Sachdev-Ye-Kitaev model,”SciPost Phys.19no. 6, (2025) 159,arXiv:2502.01582 [quant-ph]

    arXiv 2025

  25. [25]

    Nonstabilizerness Dynamics in Many-Body Localized Systems,

    P. R. N. Falcão, P. Sierant, J. Zakrzewski, and E. Tirrito, “Nonstabilizerness Dynamics in Many-Body Localized Systems,”Phys. Rev. Lett.135no. 24, (2025) 240404,arXiv:2503.07468 [quant-ph]

    arXiv 2025

  26. [26]

    Universal Spreading of Nonstabilizerness and Quantum Transport,

    E. Tirrito, P. S. Tarabunga, D. S. Bhakuni, M. Dalmonte, P. Sierant, and X. Turkeshi, “Universal Spreading of Nonstabilizerness and Quantum Transport,” arXiv:2506.12133 [quant-ph]

    Pith/arXiv arXiv

  27. [27]

    Spectral signatures of nonstabilizerness and criticality in infinite matrix product states,

    A. Hallam, R. Smith, and Z. Papić, “Spectral signatures of nonstabilizerness and criticality in infinite matrix product states,”Phys. Rev. B113no. 24, (2026) 245113, arXiv:2602.15116 [quant-ph]

    Pith/arXiv arXiv 2026

  28. [28]

    Magic and Wormholes in the Sachdev-Ye-Kitaev Model,

    V. Bettaque and B. Swingle, “Magic and Wormholes in the Sachdev-Ye-Kitaev Model,”arXiv:2602.12339 [hep-th]

    Pith/arXiv arXiv

  29. [29]

    Magic states of top quarks,

    C. D. White and M. J. White, “Magic states of top quarks,”Phys. Rev. D110no. 11, (2024) 116016,arXiv:2406.07321 [hep-ph]

    Pith/arXiv arXiv 2024

  30. [30]

    The magic of top quarks,

    C. D. White and M. J. White, “The magic of top quarks,”SciPost Phys. Proc.18 (2026) 017,arXiv:2412.07479 [hep-ph]

    arXiv 2026

  31. [31]

    Quantum magic and computational complexity in the neutrino sector,

    I. Chernyshev, C. E. P. Robin, and M. J. Savage, “Quantum magic and computational complexity in the neutrino sector,”Phys. Rev. Res.7no. 2, (2025) 023228,arXiv:2411.04203 [quant-ph]

    Pith/arXiv arXiv 2025

  32. [32]

    Harvesting stabilizer entropy and nonlocality from a quantum field,

    S. Cepollaro, S. Cusumano, A. Hamma, G. Lo Giudice, and J. Odavić, “Harvesting stabilizer entropy and nonlocality from a quantum field,”Phys. Rev. D112no. 10, (2025) 105012,arXiv:2412.11918 [quant-ph]

    arXiv 2025

  33. [33]

    Quantum magic in quantum electrodynamics,

    Q. Liu, I. Low, and Z. Yin, “Quantum magic in quantum electrodynamics,”Phys. Rev. D113no. 5, (2026) 056001,arXiv:2503.03098 [quant-ph]

    Pith/arXiv arXiv 2026

  34. [34]

    Stabilizer Rényi Entropy and Conformal Field Theory,

    M. Hoshino, M. Oshikawa, and Y. Ashida, “Stabilizer Rényi Entropy and Conformal Field Theory,”Phys. Rev. X16no. 1, (2026) 011037,arXiv:2503.13599 [quant-ph]

    arXiv 2026

  35. [35]

    Stabilizer Rényi Entropy Encodes Fusion Rules of Topological Defects and Boundaries,

    M. Hoshino and Y. Ashida, “Stabilizer Rényi Entropy Encodes Fusion Rules of Topological Defects and Boundaries,”Phys. Rev. Lett.136no. 8, (2026) 080402, arXiv:2507.10656 [quant-ph]

    arXiv 2026

  36. [36]

    Spin versus nonstabilizerness in gluon and graviton scattering,

    J. Gargalionis, N. Moynihan, S. Trifinopoulos, E. N. V. Wallace, C. D. White, and – 23 – M. J. White, “Spin versus nonstabilizerness in gluon and graviton scattering,”Phys. Rev. D113no. 1, (2026) 016007,arXiv:2508.14967 [hep-th]

    Pith/arXiv arXiv 2026

  37. [37]

    A Quantum Computational Determination of the Weak Mixing Angle in the Standard Model,

    Q. Liu, I. Low, and Z. Yin, “A Quantum Computational Determination of the Weak Mixing Angle in the Standard Model,”arXiv:2509.18251 [hep-ph]

    arXiv

  38. [38]

    Quantum Magic Reveals CP Phases Invisible to Entanglement in Spin-0 Decays,

    N. Viaux, A. Norambuena, and P. Orellana, “Quantum Magic Reveals CP Phases Invisible to Entanglement in Spin-0 Decays,”arXiv:2605.19117 [quant-ph]

    Pith/arXiv arXiv

  39. [39]

    Symmetry Breaking as Quantum Gate: Entropy and Weak Mixing Angle,

    Q.-H. Cao, Y. Liu, H. Qi, H. Zhang, and H. Zhao, “Symmetry Breaking as Quantum Gate: Entropy and Weak Mixing Angle,”arXiv:2605.22070 [hep-ph]

    Pith/arXiv arXiv

  40. [40]

    Quantum Computational Resources and Conformal Field Theory: Unifying Spins, Bosons, and Fermions,

    R. Matsuda, M. Hoshino, and Y. Ashida, “Quantum Computational Resources and Conformal Field Theory: Unifying Spins, Bosons, and Fermions,”arXiv:2607.05343 [quant-ph]

    Pith/arXiv arXiv

  41. [41]

    Magic and entanglement in 1+1-dimensional SU(2) lattice gauge theory,

    R. G. Jha, G. C. Toga, J. I. Taher, B. N. Bakalov, and A. F. Kemper, “Magic and entanglement in 1+1-dimensional SU(2) lattice gauge theory,”arXiv:2606.09971 [quant-ph]

    Pith/arXiv arXiv

  42. [42]

    Quantum Resources in Non-Abelian Lattice Gauge Theories: Nonstabilizerness, Multipartite Entanglement, and Fermionic Non-Gaussianity,

    G. C. Santra, J. Mildenberger, E. Ballini, A. Bottarelli, M. M. Wauters, and P. Hauke, “Quantum Resources in Non-Abelian Lattice Gauge Theories: Nonstabilizerness, Multipartite Entanglement, and Fermionic Non-Gaussianity,” arXiv:2510.07385 [quant-ph]

    arXiv

  43. [43]

    Exact stabilizer scars in two-dimensionalU(1)lattice gauge theory,

    S. Gupta, P. Sierant, L. Santos, and P. Stornati, “Exact stabilizer scars in two-dimensionalU(1)lattice gauge theory,”Phys. Rev. D113no. 9, (2026) 094509, arXiv:2603.03062 [quant-ph]

    Pith/arXiv arXiv 2026

  44. [44]

    Learning magic in the Schwinger model,

    S. Crew and H. H. Lu, “Learning magic in the Schwinger model,”arXiv:2508.09640 [hep-th]

    Pith/arXiv arXiv

  45. [45]

    Scattering amplitudes: the most perfect microscopic structures in the universe,

    L. J. Dixon, “Scattering amplitudes: the most perfect microscopic structures in the universe,”J. Phys. A44(2011) 454001,arXiv:1105.0771 [hep-th]

    Pith/arXiv arXiv 2011

  46. [46]

    Maximal Entanglement in High Energy Physics,

    A. Cervera-Lierta, J. I. Latorre, J. Rojo, and L. Rottoli, “Maximal Entanglement in High Energy Physics,”SciPost Phys.3(2017) 036,arXiv:1703.02989 [hep-th]

    Pith/arXiv arXiv 2017

  47. [47]

    Universality of entanglement in gluon dynamics,

    C. N. Garrido, A. Cervera-Lierta, and J. I. Latorre, “Universality of entanglement in gluon dynamics,”SciPost Phys.20no. 2, (2026) 063,arXiv:2504.15353 [hep-th]

    arXiv 2026

  48. [48]

    Entanglement Suppression and Emergent Symmetries of Strong Interactions,

    S. R. Beane, D. B. Kaplan, N. Klco, and M. J. Savage, “Entanglement Suppression and Emergent Symmetries of Strong Interactions,”Phys. Rev. Lett.122no. 10, (2019) 102001,arXiv:1812.03138 [nucl-th]

    Pith/arXiv arXiv 2019

  49. [49]

    Symmetry from entanglement suppression,

    I. Low and T. Mehen, “Symmetry from entanglement suppression,”Phys. Rev. D104 no. 7, (2021) 074014,arXiv:2104.10835 [hep-th]

    Pith/arXiv arXiv 2021

  50. [50]

    Tree-level entanglement in quantum electrodynamics,

    S. Fedida and A. Serafini, “Tree-level entanglement in quantum electrodynamics,” Phys. Rev. D107no. 11, (2023) 116007,arXiv:2209.01405 [quant-ph]

    Pith/arXiv arXiv 2023

  51. [51]

    Entropy growth in perturbative scattering,

    C. Cheung, T. He, and A. Sivaramakrishnan, “Entropy growth in perturbative scattering,”Phys. Rev. D108no. 4, (2023) 045013,arXiv:2304.13052 [hep-th]. – 24 –

    Pith/arXiv arXiv 2023

  52. [52]

    Positivity in Amplitudes and Quantum Entanglement,

    R. Aoude, G. Elor, G. N. Remmen, and O. Sumensari, “Positivity in Amplitudes and Quantum Entanglement,”Fortsch. Phys.74(2026) e70113,arXiv:2402.16956 [hep-th]

    Pith/arXiv arXiv 2026

  53. [53]

    Symmetry, entanglement, and theS-matrix,

    N. McGinnis, “Symmetry, entanglement, and theS-matrix,”arXiv:2504.21079 [hep-th]

    Pith/arXiv arXiv

  54. [54]

    Variation of Entanglement Entropy in Scattering Process,

    S. Seki, I. Y. Park, and S.-J. Sin, “Variation of Entanglement Entropy in Scattering Process,”Phys. Lett. B743(2015) 147–153,arXiv:1412.7894 [hep-th]

    Pith/arXiv arXiv 2015

  55. [55]

    Entanglement Entropy of Scattering Particles,

    R. Peschanski and S. Seki, “Entanglement Entropy of Scattering Particles,”Phys. Lett. B758(2016) 89–92,arXiv:1602.00720 [hep-th]

    Pith/arXiv arXiv 2016

  56. [56]

    Momentum-space entanglement and renormalization in quantum field theory,

    V. Balasubramanian, M. B. McDermott, and M. Van Raamsdonk, “Momentum-space entanglement and renormalization in quantum field theory,”Phys. Rev. D86(2012) 045014,arXiv:1108.3568 [hep-th]

    Pith/arXiv arXiv 2012

  57. [57]

    Area law for entanglement entropy in particle scattering,

    I. Low and Z. Yin, “Area law for entanglement entropy in particle scattering,”Phys. Rev. D113no. 6, (2026) 065004,arXiv:2405.08056 [hep-th]

    Pith/arXiv arXiv 2026

  58. [58]

    Elastic cross section is entanglement entropy,

    I. Low and Z. Yin, “Elastic cross section is entanglement entropy,”Phys. Rev. D111 no. 6, (2025) 065027,arXiv:2410.22414 [hep-th]

    Pith/arXiv arXiv 2025

  59. [59]

    Minimal entanglement and emergent symmetries in low-energy QCD,

    Q. Liu, I. Low, and T. Mehen, “Minimal entanglement and emergent symmetries in low-energy QCD,”Phys. Rev. C107no. 2, (2023) 025204,arXiv:2210.12085 [quant-ph]

    Pith/arXiv arXiv 2023

  60. [60]

    An Amplitude fornGluon Scattering,

    S. J. Parke and T. R. Taylor, “An Amplitude fornGluon Scattering,”Phys. Rev. Lett.56(1986) 2459

    1986

  61. [61]

    Perturbative gauge theory as a string theory in twistor space,

    E. Witten, “Perturbative gauge theory as a string theory in twistor space,”Commun. Math. Phys.252(2004) 189–258,arXiv:hep-th/0312171

    Pith/arXiv arXiv 2004

  62. [62]

    MHV vertices and tree amplitudes in gauge theory,

    F. Cachazo, P. Svrcek, and E. Witten, “MHV vertices and tree amplitudes in gauge theory,”JHEP09(2004) 006,arXiv:hep-th/0403047

    Pith/arXiv arXiv 2004

  63. [63]

    New recursion relations for tree amplitudes of gluons,

    R. Britto, F. Cachazo, and B. Feng, “New recursion relations for tree amplitudes of gluons,”Nucl. Phys. B715(2005) 499–522,arXiv:hep-th/0412308

    Pith/arXiv arXiv 2005

  64. [64]

    Direct proof of tree-level recursion relation in Yang-Mills theory,

    R. Britto, F. Cachazo, B. Feng, and E. Witten, “Direct proof of tree-level recursion relation in Yang-Mills theory,”Phys. Rev. Lett.94(2005) 181602, arXiv:hep-th/0501052

    Pith/arXiv arXiv 2005

  65. [65]

    A Relation Between Tree Amplitudes of Closed and Open Strings,

    H. Kawai, D. C. Lewellen, and S. H. H. Tye, “A Relation Between Tree Amplitudes of Closed and Open Strings,”Nucl. Phys. B269(1986) 1–23

    1986

  66. [66]

    New Relations for Gauge-Theory Amplitudes,

    Z. Bern, J. J. M. Carrasco, and H. Johansson, “New Relations for Gauge-Theory Amplitudes,”Phys. Rev. D78(2008) 085011,arXiv:0805.3993 [hep-ph]

    Pith/arXiv arXiv 2008

  67. [67]

    Perturbative Quantum Gravity as a Double Copy of Gauge Theory,

    Z. Bern, J. J. M. Carrasco, and H. Johansson, “Perturbative Quantum Gravity as a Double Copy of Gauge Theory,”Phys. Rev. Lett.105(2010) 061602, arXiv:1004.0476 [hep-th]. – 25 –

    Pith/arXiv arXiv 2010

  68. [68]

    The duality between color and kinematics and its applications,

    Z. Bern, J. J. Carrasco, M. Chiodaroli, H. Johansson, and R. Roiban, “The duality between color and kinematics and its applications,”J. Phys. A57no. 33, (2024) 333002,arXiv:1909.01358 [hep-th]

    Pith/arXiv arXiv 2024

  69. [69]

    Entanglement and quantum tomography with top quarks at the LHC,

    Y. Afik and J. R. M. de Nova, “Entanglement and quantum tomography with top quarks at the LHC,”Eur. Phys. J. Plus136no. 9, (2021) 907,arXiv:2003.02280 [quant-ph]. [70]A TLASCollaboration, G. Aadet al., “Observation of quantum entanglement with top quarks at the ATLAS detector,”Nature633no. 8030, (2024) 542–547, arXiv:2311.07288 [hep-ex]. [71]CMSCollaborat...

    Pith/arXiv arXiv 2021

  70. [72]

    Quantum entanglement and Bell inequality violation at colliders,

    A. J. Barr, M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Marzola, “Quantum entanglement and Bell inequality violation at colliders,”Prog. Part. Nucl. Phys.139 (2024) 104134,arXiv:2402.07972 [hep-ph]

    Pith/arXiv arXiv 2024

  71. [73]

    Quantum Tomography of Fermion Pairs in e+e− Collisions: Longitudinal Beam Polarization Effects,

    Y.-C. Guo, T. Han, M. Low, and Y. Su, “Quantum Tomography of Fermion Pairs in e+e− Collisions: Longitudinal Beam Polarization Effects,”arXiv:2602.02719 [hep-ph]

    arXiv

  72. [74]

    Non-local nonstabiliserness in Gluon and Graviton Scattering,

    J. Gargalionis, N. Moynihan, M. L. Reichenberg Ashby, E. N. V. Wallace, C. D. White, and M. J. White, “Non-local nonstabiliserness in Gluon and Graviton Scattering,”arXiv:2603.04148 [hep-th]

    arXiv

  73. [75]

    The nonlocal magic of a holographic Schwinger pair,

    S. Grieninger, “The nonlocal magic of a holographic Schwinger pair,” arXiv:2605.04210 [hep-th]

    Pith/arXiv arXiv

  74. [76]

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

    G. Busoni, J. Gargalionis, E. N. V. Wallace, and M. J. White, “Emergent symmetry in a two-Higgs-doublet model from quantum information and nonstabilizerness,” Phys. Rev. D112no. 3, (2025) 035022,arXiv:2506.01314 [hep-ph]

    Pith/arXiv arXiv 2025

  75. [77]

    Probing new physics in the top sector using quantum information,

    R. Aoude, H. Banks, C. D. White, and M. J. White, “Probing new physics in the top sector using quantum information,”Phys. Rev. D113no. 11, (2026) 115066, arXiv:2505.12522 [hep-ph]

    Pith/arXiv arXiv 2026

  76. [78]

    Quantum complexity fluctuations from nuclear and hypernuclear forces,

    C. E. P. Robin and M. J. Savage, “Quantum complexity fluctuations from nuclear and hypernuclear forces,”Phys. Rev. C112no. 4, (2025) 044004, arXiv:2405.10268 [nucl-th]

    arXiv 2025

  77. [79]

    Local Minimum of Spin-Sector Magic at the CP-Conserving Point in Low-Energy Neutron-Proton Scattering,

    C. Li, T. Ma, and M. Zhu, “Local Minimum of Spin-Sector Magic at the CP-Conserving Point in Low-Energy Neutron-Proton Scattering,”arXiv:2606.31501 [hep-ph]

    Pith/arXiv arXiv

  78. [80]

    Collective neutrino oscillations: Many-body non-forward effects and non-classicality,

    J. Froustey, E. Rrapaj, Y. Liu, G. Li, C. Iancu, and V. Cirigliano, “Collective neutrino oscillations: Many-body non-forward effects and non-classicality,” arXiv:2606.12404 [hep-ph]

    Pith/arXiv arXiv

  79. [81]

    Quantum Complexity and New Directions in – 26 – Nuclear Physics and High-Energy Physics Phenomenology,

    C. E. P. Robin and M. J. Savage, “Quantum Complexity and New Directions in – 26 – Nuclear Physics and High-Energy Physics Phenomenology,”arXiv:2604.26376 [quant-ph]

    Pith/arXiv arXiv

  80. [82]

    Automated computation of spin-density matrices and quantum observables for collider physics,

    V. Durupt, F. Maltoni, and O. Mattelaer, “Automated computation of spin-density matrices and quantum observables for collider physics,”JHEP04(2026) 103, arXiv:2510.17730 [hep-ph]

    Pith/arXiv arXiv 2026

Showing first 80 references.