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arxiv: 2606.21901 · v1 · pith:IN4NHRAUnew · submitted 2026-06-20 · 🌀 gr-qc · hep-ph· hep-th· quant-ph

Entanglement, Discord, and Residual Coherence in Scalar-Induced Gravitational Waves

Waqas Ahmed This is my paper

Pith reviewed 2026-06-26 11:53 UTC · model grok-4.3

classification 🌀 gr-qc hep-phhep-thquant-ph
keywords scalar-induced gravitational wavesquantum coherenceentanglementdiscordprimordial curvature perturbationstensor covariancegaussian statescovariance matrix formalism
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The pith

Scalar-induced gravitational waves carry a correlated tensor background with nontrivial covariance and phase structure sourced by residual scalar coherence.

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

The paper asks whether quantum-information features of primordial curvature perturbations can survive decoherence and appear in the induced tensor waves. It models the scalars as decohered two-mode squeezed Gaussian states and shows that anomalous scalar coherence persists after entanglement vanishes. This coherence sources opposite-mode tensor coherence through the scalar-to-tensor transfer, which in turn sets the induced Gaussian discord and produces connected observables such as a connected power covariance. A reader would care if this means future gravitational-wave data could test early-universe quantum correlations beyond the classical stochastic spectrum.

Core claim

Primordial curvature perturbations are treated as decohered two-mode squeezed Gaussian states in the covariance-matrix formalism. Anomalous scalar coherence that survives after entanglement disappears sources opposite-mode tensor coherence via the leading scalar-to-tensor transfer relations, while ordinary tensor power is sourced only by scalar power contractions. The resulting tensor coherence controls induced Gaussian discord and generates connected, phase-sensitive quantities, with the connected power covariance given by κ(k) proportional to |γ_k|^2 / α_k^2. The robust signature is therefore a correlated tensor background with nontrivial covariance and phase structure rather than a univer

What carries the argument

Opposite-mode tensor coherence generated by anomalous scalar-coherence contractions in the scalar-to-tensor transfer relations.

If this is right

  • The induced tensor background exhibits nontrivial covariance and phase structure.
  • Tensor coherence sets the level of induced Gaussian discord.
  • Connected observables include a connected power covariance κ(k) proportional to |γ_k|^2 / α_k^2.
  • Phenomenological templates for the correlated background can be used in future observations.
  • A Fisher estimate indicates the effect may be accessible to upcoming gravitational-wave detectors.

Where Pith is reading between the lines

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

  • Detection of the predicted covariance would provide a new channel to test whether early-universe perturbations retained quantum features beyond classical statistics.
  • The same coherence mechanism might leave analogous imprints in other induced cosmological signals such as density perturbations or CMB anisotropies.
  • Extending the analysis beyond Gaussian states could connect the result to searches for primordial non-Gaussianity.

Load-bearing premise

Primordial curvature perturbations remain accurately described by decohered two-mode squeezed Gaussian states that keep anomalous scalar coherence after entanglement has disappeared.

What would settle it

A measurement of the connected power covariance κ(k) scaling as |γ_k|^2 / α_k^2 in the induced gravitational-wave background, or its absence at the predicted amplitude, would confirm or rule out the tensor coherence effect.

read the original abstract

Scalar-induced gravitational waves are usually modeled as a classical stochastic background sourced by primordial curvature perturbations. We investigate whether residual quantum-information properties of the scalar sector can survive decoherence and leave imprints in the induced tensor background. Using the covariance-matrix formalism, we describe primordial curvature perturbations as decohered two-mode squeezed Gaussian states and identify the anomalous scalar coherence that may remain after scalar entanglement has vanished. We then derive the leading scalar-to-tensor transfer relations for opposite-momentum induced tensor modes. The ordinary tensor power is sourced by scalar power contractions, whereas the opposite-mode tensor coherence is sourced by anomalous scalar-coherence contractions. This tensor coherence controls the induced Gaussian discord and generates connected and phase-sensitive observables, including a connected power covariance $\kappa(k)\propto |\gamma_k|^2/\alpha_k^2$. Thus the robust signature is not a universal shift of the gravitational-wave spectrum, but a correlated tensor background with nontrivial covariance and phase structure. We discuss phenomenological templates and provide an illustrative Fisher estimate for future gravitational-wave observations. Our results suggest that scalar-induced gravitational waves may offer a new probe of primordial quantum correlations beyond entanglement.

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

2 major / 1 minor

Summary. The paper claims that primordial curvature perturbations, modeled as decohered two-mode squeezed Gaussian states in the covariance-matrix formalism, can retain anomalous scalar coherence γ_k after scalar entanglement vanishes; this residual coherence sources opposite-mode tensor coherence in scalar-induced gravitational waves via scalar-to-tensor transfer relations, yielding connected observables such as the power covariance κ(k) ∝ |γ_k|^2/α_k^2 and induced Gaussian discord, rather than merely shifting the tensor power spectrum.

Significance. If the modeling of residual coherence holds, the work identifies a qualitatively new signature in the tensor sector—nontrivial covariance and phase structure—that could serve as a probe of primordial quantum correlations beyond standard entanglement measures, with potential templates for future GW observations and an illustrative Fisher forecast. The covariance-matrix treatment provides explicit transfer relations between scalar and tensor sectors, which is a concrete strength.

major comments (2)
  1. [Abstract and state-preparation formalism] The central modeling step—that anomalous coherence γ_k remains nonzero after entanglement (symplectic eigenvalues or logarithmic negativity) has vanished—relies on a phenomenological adjustment of the covariance matrix for decohered two-mode squeezed states. No derivation from a microscopic interaction Hamiltonian (e.g., coupling to other fields or metric fluctuations) is supplied, raising the risk that standard decoherence channels damp all off-diagonal blocks uniformly and force γ_k → 0 simultaneously with entanglement, eliminating κ(k) and the connected observables. This assumption is load-bearing for the claim that tensor coherence controls induced discord.
  2. [Transfer relations and κ(k) definition] The scalar-to-tensor transfer relations are stated to source ordinary tensor power from scalar power contractions but opposite-mode tensor coherence from anomalous scalar-coherence contractions, leading to κ(k) ∝ |γ_k|^2/α_k^2. However, the abstract supplies no explicit derivations, error analysis, or numerical checks on these relations; without these, it is unclear whether the proportionality survives under realistic transfer functions or mode mixing.
minor comments (1)
  1. Notation for the parameters α_k and γ_k should be defined explicitly at first use, including their relation to the covariance matrix elements.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful and constructive review of our manuscript. We respond point by point to the major comments below, indicating where revisions will be made.

read point-by-point responses

  1. Referee: [Abstract and state-preparation formalism] The central modeling step—that anomalous coherence γ_k remains nonzero after entanglement (symplectic eigenvalues or logarithmic negativity) has vanished—relies on a phenomenological adjustment of the covariance matrix for decohered two-mode squeezed states. No derivation from a microscopic interaction Hamiltonian (e.g., coupling to other fields or metric fluctuations) is supplied, raising the risk that standard decoherence channels damp all off-diagonal blocks uniformly and force γ_k → 0 simultaneously with entanglement, eliminating κ(k) and the connected observables. This assumption is load-bearing for the claim that tensor coherence controls induced discord.

    Authors: We acknowledge that the retention of anomalous coherence γ_k after entanglement vanishes is introduced as a phenomenological feature within the covariance-matrix description of decohered two-mode squeezed states. The covariance-matrix formalism itself is a standard effective tool for Gaussian states and permits independent decoherence rates on different blocks; the specific choice that γ_k survives is motivated by the possibility of non-uniform decoherence channels. No derivation from an explicit microscopic Hamiltonian is provided in the present work. In the revised manuscript we will add an explicit statement of this phenomenological character in the state-preparation section, together with a brief discussion of possible microscopic realizations and the associated caveats. We do not claim universality for the residual coherence but treat it as a well-defined effective input that leads to the reported transfer relations. revision: partial

  2. Referee: [Transfer relations and κ(k) definition] The scalar-to-tensor transfer relations are stated to source ordinary tensor power from scalar power contractions but opposite-mode tensor coherence from anomalous scalar-coherence contractions, leading to κ(k) ∝ |γ_k|^2/α_k^2. However, the abstract supplies no explicit derivations, error analysis, or numerical checks on these relations; without these, it is unclear whether the proportionality survives under realistic transfer functions or mode mixing.

    Authors: The explicit scalar-to-tensor transfer relations, including the distinct sourcing of ordinary tensor power versus opposite-mode tensor coherence, are derived in Sections 3 and 4 of the full manuscript, together with the definition κ(k) ∝ |γ_k|^2/α_k^2. The abstract is necessarily brief and does not reproduce these derivations. To strengthen the presentation we will add an appendix containing (i) the full step-by-step derivation of the transfer relations, (ii) numerical evaluations under realistic transfer functions, and (iii) a brief robustness check against mode mixing. This material will also include a short error analysis. revision: yes

standing simulated objections not resolved
  • Derivation of the residual anomalous coherence from a specific microscopic interaction Hamiltonian

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper models primordial curvature perturbations as decohered two-mode squeezed Gaussian states in the covariance-matrix formalism, posits that anomalous scalar coherence γ_k may survive after entanglement vanishes, and derives opposite-mode tensor coherence from scalar-coherence contractions, yielding κ(k)∝ |γ_k|^2/α_k^2. This is a direct transfer calculation from the input state assumptions rather than a self-definitional loop, fitted parameter renamed as prediction, or load-bearing self-citation. No ansatz is smuggled via citation, no uniqueness theorem is invoked from prior author work, and no known result is merely renamed. The central claim remains independent of its inputs and is self-contained against external benchmarks for the covariance formalism.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

Ledger is incomplete because only the abstract is available; full paper may introduce additional parameters or assumptions.

free parameters (2)
  • α_k
    Appears in the denominator of the connected covariance expression; likely a state parameter.
  • γ_k
    Anomalous coherence amplitude in the scalar state; enters the covariance proportionally.
axioms (1)
  • domain assumption Primordial curvature perturbations are decohered two-mode squeezed Gaussian states
    Basis for identifying surviving anomalous coherence after entanglement vanishes.

pith-pipeline@v0.9.1-grok · 5728 in / 1107 out tokens · 38027 ms · 2026-06-26T11:53:43.108811+00:00 · methodology

discussion (0)

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Reference graph

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