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arxiv: 2510.04200 · v2 · submitted 2025-10-05 · ✦ hep-ph · hep-th· quant-ph

Qubit entanglement from forward scattering

Kamila Kowalska , Enrico Maria Sessolo This is my paper

Pith reviewed 2026-05-18 10:23 UTC · model grok-4.3

classification ✦ hep-ph hep-thquant-ph
keywords qubit entanglementforward scatteringrelativistic scatteringconcurrenceS-matrixtwo-Higgs doublet modelelectron-positron annihilationlinearized entropy
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0 comments X

The pith

The real part of the inelastic forward amplitude fixes the leading concurrence of scattered qubits after tracing momenta.

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

The paper derives an analytic expression for the concurrence between two discrete quantum numbers treated as qubits in the final state of a relativistic 2 to 2 scattering process. After the full density matrix is evolved with the perturbative S-matrix and the continuous momentum degrees of freedom are integrated out, the resulting mixed two-qubit state has a concurrence that, for any initial product state, depends at leading order only on the real part of the inelastic forward amplitude and on the initial state. The same real part supplies a subleading reduction in the linearized entropy of the final state, an amount that equals the relative entropy of coherence when the initial state belongs to the computational basis. The result is illustrated with high-energy scalar scattering in the two-Higgs-doublet model and with electron-positron annihilation.

Core claim

Given an initial product state, the concurrence of the mixed final qubit state obtained by tracing momentum degrees of freedom out of the full density matrix in perturbative 2 to 2 scattering depends at leading order only on the real part of the inelastic forward amplitude and on the initial state.

What carries the argument

The reduced two-qubit density matrix formed by integrating the S-matrix-evolved final-state density matrix over all continuous momentum variables; its concurrence isolates the real part of the inelastic forward amplitude at leading perturbative order.

If this is right

  • Entanglement generated in scattering becomes predictable from standard forward-scattering data without needing the full differential cross section.
  • In the two-Higgs-doublet model the concurrence for high-energy scalar scattering is fixed by the model's couplings through the forward amplitude.
  • In electron-positron annihilation the final-state concurrence follows directly from the electromagnetic forward amplitude.
  • The real part of the forward amplitude reduces linearized entropy by an amount equal to the relative entropy of coherence for computational-basis initial states.

Where Pith is reading between the lines

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

  • The relation may offer a new experimental handle on the real parts of amplitudes that are otherwise hard to isolate from cross sections alone.
  • Similar momentum-tracing procedures could connect entanglement measures to other S-matrix quantities such as total cross sections via the optical theorem.
  • Collider tests would require preparing specific initial polarization states and reconstructing correlations among the discrete quantum numbers of the final particles.

Load-bearing premise

Tracing over the continuous momentum degrees of freedom produces a well-defined mixed qubit density matrix whose entanglement properties are captured by the leading term in the perturbative S-matrix expansion.

What would settle it

A direct measurement of final-state qubit concurrence for a prepared initial product state in high-energy 2 to 2 scattering that differs from the numerical value computed from the real part of the inelastic forward amplitude.

read the original abstract

In the context of entanglement in relativistic $2\to 2$ scattering described by a perturbative $S$-matrix, we derive analytically the concurrence for a mixed final state of two qubits corresponding to a discrete quantum number of the scattered particles. The qubit density matrix is obtained by tracing the momentum degrees of freedom out of the full density matrix of the scattered system. Given an initial product state, the derived concurrence depends at the leading order on the real part of the inelastic forward amplitude and the initial state only. We also point out that the real part of the forward amplitude provides a subleading correction to the linearized entropy, reducing it by an amount that, for a computational-basis state, is equivalent to the relative entropy of coherence. We illustrate our findings with two examples of phenomenological interest: high-energy scattering of two scalar fields in the two-Higgs doublet model, and high-energy electron-positron annihilation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript derives an analytical expression for the concurrence of a mixed two-qubit state arising from the discrete quantum numbers in a relativistic 2→2 scattering process. The qubit density matrix is obtained by tracing over the continuous momentum degrees of freedom in the final state density matrix constructed from the perturbative S-matrix. For an initial product state, the leading-order concurrence is found to depend solely on the real part of the inelastic forward scattering amplitude and the initial state. Additionally, the real part of the forward amplitude is shown to provide a subleading correction to the linearized entropy, which for computational basis states corresponds to the relative entropy of coherence. The results are illustrated with examples in the two-Higgs-doublet model and electron-positron annihilation.

Significance. If the derivation of the reduced density matrix holds, the work provides a parameter-free analytical connection between qubit concurrence and the real part of the inelastic forward amplitude in perturbative relativistic scattering. This offers a potential bridge between quantum information measures and standard S-matrix techniques in high-energy physics, with possible relevance to collider observables. The absence of free parameters, ad-hoc axioms, or invented entities strengthens the result, as does the explicit link to relative entropy of coherence. The significance would be enhanced by explicit validation of the tracing procedure.

major comments (1)
  1. [Abstract, paragraph 2] Abstract (paragraph 2) and the derivation of the reduced density matrix: The claim that the concurrence depends at leading order only on Re(T_inelastic forward) and the initial state requires that tracing over continuous final-state momenta produces a well-defined, positive semi-definite 4×4 qubit density matrix. The S-matrix elements contain four-momentum delta functions; the off-diagonal interference terms therefore involve integrals over the final momentum measure that are formally singular or distribution-valued at leading order. The manuscript should supply an explicit regularization (wave-packet smearing or principal-value prescription) and verify that the resulting matrix is trace-class, Hermitian, and positive, with off-diagonal elements isolating the real part of the forward amplitude.
minor comments (1)
  1. [Examples section] The two phenomenological examples (2HDM scalar scattering and e+e− annihilation) would benefit from a brief statement of the specific kinematic regime and coupling values used to evaluate the forward amplitude.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comment on the technical details of the reduced density matrix. We address the point below and have revised the manuscript to incorporate an explicit regularization procedure.

read point-by-point responses

  1. Referee: [Abstract, paragraph 2] Abstract (paragraph 2) and the derivation of the reduced density matrix: The claim that the concurrence depends at leading order only on Re(T_inelastic forward) and the initial state requires that tracing over continuous final-state momenta produces a well-defined, positive semi-definite 4×4 qubit density matrix. The S-matrix elements contain four-momentum delta functions; the off-diagonal interference terms therefore involve integrals over the final momentum measure that are formally singular or distribution-valued at leading order. The manuscript should supply an explicit regularization (wave-packet smearing or principal-value prescription) and verify that the resulting matrix is trace-class, Hermitian, and positive, with off-diagonal elements isolating the real part of the forward amplitude.

    Authors: We agree that a rigorous treatment of the momentum integrals is required to substantiate the tracing procedure. In the revised manuscript we introduce an explicit regularization by representing the initial two-particle state as a product of narrow Gaussian wave packets in momentum space (with width parameter σ). The final-state momentum integrals are then performed with this smearing; after the trace is taken we take the limit σ → 0 while keeping the on-shell conditions. This procedure yields a well-defined 4×4 Hermitian matrix whose off-diagonal elements are proportional to the real part of the inelastic forward amplitude (the imaginary part is absorbed into the diagonal entries via the optical theorem). We explicitly verify that the matrix remains trace-class, positive semi-definite, and normalized to unity for the kinematic regimes considered. The leading-order concurrence is unaffected by the regularization. These additions appear in a new subsection of Section II and in Appendix B. revision: yes

Circularity Check

0 steps flagged

No circularity: concurrence derived directly from perturbative S-matrix without reduction to inputs or self-citation

full rationale

The paper analytically derives the concurrence of the reduced two-qubit density matrix (obtained by tracing continuous momenta from the full S-matrix evolution of an initial product state) at leading perturbative order. This dependence on Re(T_inelastic forward) and the initial state follows from the structure of the off-diagonal coherent terms in the S-matrix elements after integration, without the forward amplitude being defined via the concurrence or any fitted parameter being relabeled as a prediction. No load-bearing self-citations, uniqueness theorems, or ansatze from prior author work are invoked to force the result; the derivation remains self-contained against the S-matrix expansion and partial-trace operation as stated in the abstract and derivation sections.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the perturbative S-matrix framework for 2→2 scattering and the legitimacy of obtaining a qubit density matrix by partial trace over momenta; no free parameters or new entities are introduced in the abstract.

axioms (2)
  • domain assumption The S-matrix is perturbative and the leading-order forward amplitude is well-defined for inelastic channels.
    Invoked in the abstract to obtain the concurrence at leading order.
  • domain assumption Tracing out continuous momentum degrees of freedom yields a valid mixed state on the discrete qubit subspace.
    Required to define the qubit density matrix whose concurrence is computed.

pith-pipeline@v0.9.0 · 5677 in / 1272 out tokens · 27491 ms · 2026-05-18T10:23:30.713287+00:00 · methodology

discussion (0)

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Forward citations

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Reference graph

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