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Infrared Quantum-Environmental Engineering Using Soft Photons as Angular-Momentum Detectors

Soo-Jong Rey

Published Jul 23, 2026• 0 citations
Publisher

Abstract

Built upon infrared QED formulated as an open quantum system, I use the complementary soft photons as a quantum instrument. The experiment selects the hard-state code, resolved process, trajectory, accepted modes, and photon readout. QED fixes the interaction. On an eikonal-degenerate reducing code, the momentum-flow jump acts as a scalar. A Lindbladian displacement removes this common term from the dissipator. Its interference with the Low--Burnett--Kroll operator enters a finite Hamiltonian. The residual dissipator ${\cal J}_\lambda(\hat q)$ measures direction- and helicity-dependent projections of orbital and spin angular momentum. I isolate the same operator in a selective photon measurement by coherently nulling the branch-independent eikonal output. The nulled click effects and the logical dissipator scale as $E_d^2$. Both saturate at the lower infrared endpoint. In the semiclassical branch limit, the decoherence functional$$ \Gamma^{(1)}_{ab}(E_d)= \frac{e^2}{2}\sum_{\lambda=\pm}\int_0^{E_d} \frac{{\rm d}^3q}{(2\pi)^3 2\omega} \left|{\cal J}_{\lambda,a}(\hat q)-{\cal J}_{\lambda,b}(\hat q)\right|^2$$sets the soft-output overlap. Coherent prescribed currents exponentiate this functional. Repeated outputs give the exact sample complexity for hard-branch identification. General mixed outputs obey the quantum Chernoff bound. I also specialize privacy--correctability duality to the vacuum-plus-one-photon instrument. The resulting criterion identifies hard codes that hide their logical state from the retained soft output.I extend the instrument to orthogonal mode restrictions and zero-mean Gaussian soft states. I prove covariance under unitary mode transformations. I derive the equivalent positive noise-kernel form. The result promotes the finite two-path record to an operator-valued QED instrument. Soft radiation becomes a controlled probe of angular momentum.

DOI
10.5281/zenodo.21501494

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Built upon infrared QED formulated as an open quantum system, I use the complementary soft photons as a quantum instrument. The experiment selects the hard-state code, resolved process, trajectory, accepted modes, and photon readout. QED fixes the interaction. On an eikonal-degenerate reducing code, the momentum-flow jump acts as a scalar. A Lindbladian displacement removes this common term from the dissipator. Its interference with the Low--Burnett--Kroll operator enters a finite Hamiltonian. The residual dissipator Jλ(q^){\cal J}_\lambda(\hat q)Jλ​(q^​) measures direction- and helicity-dependent projections of orbital and spin angular momentum. I isolate the same operator in a selective photon measurement by coherently nulling the branch-independent eikonal output. The nulled click effects and the logical dissipator scale as Ed2E_d^2Ed2​. Both saturate at the lower infrared endpoint. In the semiclassical branch limit, the decoherence functionalΓab(1)(Ed)=e22∑λ=±∫0Edd3q(2π)32ω∣Jλ,a(q^)−Jλ,b(q^)∣2 \Gamma^{(1)}_{ab}(E_d)= \frac{e^2}{2}\sum_{\lambda=\pm}\int_0^{E_d} \frac{{\rm d}^3q}{(2\pi)^3 2\omega} \left|{\cal J}_{\lambda,a}(\hat q)-{\cal J}_{\lambda,b}(\hat q)\right|^2Γab(1)​(Ed​)=2e2​∑λ=±​∫0Ed​​(2π)32ωd3q​∣Jλ,a​(q^​)−Jλ,b​(q^​)∣2sets the soft-output overlap. Coherent prescribed currents exponentiate this functional. Repeated outputs give the exact sample complexity for hard-branch identification. General mixed outputs obey the quantum Chernoff bound. I also specialize privacy--correctability duality to the vacuum-plus-one-photon instrument. The resulting criterion identifies hard codes that hide their logical state from the retained soft output.I extend the instrument to orthogonal mode restrictions and zero-mean Gaussian soft states. I prove covariance under unitary mode transformations. I derive the equivalent positive noise-kernel form. The result promotes the finite two-path record to an operator-valued QED instrument. Soft radiation becomes a controlled probe of angular momentum.
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I derive the charged-particle spectral edge from the quantum instrument of soft QED. I use two projections of that instrument. Tracing over unresolved photons gives the reduced hard-sector channel. Pushing the outcomes to total energy gives the inclusive energy distribution. Its Laplace exponent is fixed by the diagonal soft intensity. For dNh(ω)=ηhdω/ω+dNh,reg(ω){\rm d} N_h(ω)=η_h{\rm d}ω/ω+{\rm d} N_{h,\mathrm{reg}}(ω)dNh​(ω)=ηh​dω/ω+dNh,reg​(ω), I obtain ρinc(s)∼Cθ(s−m2)(s−m2)−1+ηhρ_{\mathrm{inc}}(s)\sim Cθ(s-m^2)(s-m^2)^{-1+η_h}ρinc​(s)∼Cθ(s−m2)(s−m2)−1+ηh​. I retain the coherence kernel and derive hard-sector dephasing and the spectral edge from two contractions of one soft environment. The diagonal coefficient κaaκ_{aa}κaa​ fixes the endpoint exponent, while 12(κaa+κbb−2Re⁡κba)\frac12(κ_{aa}+κ_{bb}-2\operatorname{Re}κ_{ba})21​(κaa​+κbb​−2Reκba​) fixes the dephasing exponent between hard alternatives. I then classify infrared energy marginals, derive the finite-resolution residue Z(μ)=(μ/Λ)ηhZ(μ)=(μ/Λ)^{η_h}Z(μ)=(μ/Λ)ηh​, prove stability under infrared-integrable perturbations, and separate the bath exponent from a hard threshold exponent. For the one-electron spectral measure, the hard threshold factor is regular. The resulting edge has the local power law of a gapped unparticle spectrum, while its exponent remains a response coefficient of the unresolved photon sector.
The discard ZX-calculus, a diagrammatic language for mixed-state quantum mechanics, is used to give a nonperturbative, categorical proof of the Bloch-Nordsieck cancellation of infrared divergences in QED. Soft photons are treated as an open quantum system: the resolved charged particles and hard photons form the system, while photons below a detector resolution form the environment. The reduced hard channel is a completely positive trace-preserving (CPTP) map, and the soft-photon theorem replaces the full S-matrix by a controlled displacement operator whose Feynman-Vernon influence functional satisfies the equal-history normalization ${\cal F}[J,J]=1 $. In the ZX-calculus, this normalization is a single diagrammatic identity: the doubled displacement diagram collapses to the bare wire under the unitarity, cyclicity, and discard rules. The proof therefore serves as a categorical consistency check on the open-system treatment of soft QED given in a companion paper; it confirms that the physical derivation is logically complete and free of hidden assumptions about the infrared limit. For off-diagonal hard-state elements, the same diagram yields the coherent-state overlap, giving a first-principles account of soft-cloud decoherence. The soft-shell coarse graining is then constructed as a CPTP Schur channel whose infinitesimal limit produces the exact Lindblad generator with jump operators determined by the eikonal emission amplitudes. Finally, a local CPTP-certification pipeline is developed for non-Markovian process tensors, enabling constant-time verification of trace preservation in open quantum simulations. The framework bridges categorical quantum semantics, non-equilibrium field theory, and practical open-system compilation.
Quantum optical and photonic platforms are undergoing a convergent transition: across microresonator nonlinear optics, attosecond interferometry, atom-optic inertial sensors, macroscopic mechanical oscillators, and molecular cavity optomechanics, the central engineering challenge is not merely generating non-classical light but *controlling the photon-statistics and coherence structure* of the resulting states under realistic loss, decoherence, and measurement back-action. This paper synthesizes six to seven recent arXiv preprints from the physics.optics and quant-ph categories to argue — as a heuristic reading, not a derivation — that a shared structural pattern governs these platforms: **the interplay between a nonlinear or interferometric resource that generates non-Gaussian photon statistics, and a decoherence or dephasing channel that selectively degrades specific coherence components, creating an operational tradeoff that can be navigated by mode-selection, state-conditioning, or counterdiabatic control**. Concretely, we draw on findings spanning Kerr microresonator pump-depletion dynamics and Wigner-negativity generation [corpus:arxiv:2606.19085], attosecond path-qubit coherence loss in high-harmonic generation [corpus:arxiv:2606.20372], spatiotemporally structured spontaneous parametric down-conversion [corpus:arxiv:2606.19219], twin-beam quantum LiDAR under correlated noise [corpus:arxiv:2606.17908], EPR correlations between macroscopic mechanical oscillators via SU(1,1) interferometry [corpus:arxiv:2606.18202], frequency upconversion in molecular cavity optomechanical systems with gain [corpus:arxiv:2606.17877], and counterdiabatic Raman atom optics for compact gravimetry [corpus:arxiv:2606.16945]. The falsification path for the central thesis is direct: if any of these platforms exhibits non-Gaussian state generation or sensing enhancement that is *insensitive* to the specific coherence-loss channel — i.e., where the resource survives regardless of mode-selection or conditioning strategy — the heuristic unification collapses. We identify concrete experimental tests for each sub-claim. --- Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2606.16945, 2606.17877, 2606.17908, 2606.18202, 2606.19085, 2606.19219, 2606.20372
We revisit gravitational decoherence of matter superpositions using the leading soft sector of the graviton SSS-matrix. Starting from Weinberg's soft theorem and the overlap of coherent radiation states, we derive, for branch configurations with the same total four-momentum, a gauge-invariant, nonnegative leading-soft decoherence exponent and evaluate the polarization sum and angular integrals exactly at this order. In the vacuum, coherence between branches with distinguishable soft radiation vanishes as the infrared cutoff is removed. The leading nonrelativistic term is purely quadrupolar as a consequence of energy--momentum conservation. We extend the analysis to single- and two-mode squeezed graviton states, including the two-mode case motivated by inflation. Squeezing can enhance or suppress decoherence depending on the relative phase, while phase averaging gives an enhancement governed by the graviton occupation. For a phase-averaged relic background with an approximately flat energy-density spectrum over the relevant soft frequency band, the sharp-cutoff identification of the infrared scale with the inverse observation time gives a contribution that grows with the gravitational-wave energy density and with the fourth power of the observation time. These results connect soft-graviton scattering, infrared quantum information, and decoherence in nonvacuum gravitational backgrounds.