After Q_s-adaptive coarse graining, conditional gluon Husimi momentum distributions from fixed-coupling SO(3)-BK evolution collapse as functions of k/Q_s(Y,b), with conditional entropy growing at unit slope versus ⟨ln Q_s²⟩.
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Deep inelastic scattering as a probe of entanglement
14 Pith papers cite this work, alongside 211 external citations. Polarity classification is still indexing.
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Pith papers citing it
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abstract
Using non-linear evolution equations of QCD, we compute the von Neumann entropy of the system of partons resolved by deep inelastic scattering at a given Bjorken $x$ and momentum transfer $q^2 = - Q^2$. We interpret the result as the entropy of entanglement between the spatial region probed by deep inelastic scattering and the rest of the proton. At small $x$ the relation between the entanglement entropy $S(x)$ and the parton distribution $xG(x)$ becomes very simple: $S(x) = \ln[ xG(x) ]$. In this small $x$, large rapidity $Y$ regime, all partonic micro-states have equal probabilities -- the proton is composed by an exponentially large number $\exp(\Delta Y)$ of micro-states that occur with equal and exponentially small probabilities $\exp(-\Delta Y)$, where $\Delta$ is defined by $xG(x) \sim 1/x^\Delta$. For this equipartitioned state, the entanglement entropy is maximal -- so at small $x$, deep inelastic scattering probes a {\it maximally entangled state}. We propose the entanglement entropy as an observable that can be studied in deep inelastic scattering. This will require event-by-event measurements of hadronic final states, and would allow to study the transformation of entanglement entropy into the Boltzmann one. We estimate that the proton is represented by the maximally entangled state at $x \leq 10^{-3}$; this kinematic region will be amenable to studies at the Electron Ion Collider.
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background 4representative citing papers
Subleading soft-gluon recoil rotates the heavy-quark spin-correlation plane; tracing over unresolved radiation dephases in-plane coherences while protecting the normal-axis correlation.
A reciprocal symmetry z↔1/z is identified in KNO scaling violations in pp collisions at 7-13 TeV, imposing P'(<n>)=-P(<n>)/<n> and enabling entanglement entropy extraction from the central multiplicity region.
Quantum systems reach a Maximal Entanglement Limit where entanglement geometry produces thermal reduced density matrices and probabilistic behavior in statistical and high-energy physics.
In unquenched scalar Yukawa theory, parton entanglement entropy encodes quantum information that cannot be reduced to Shannon entropy of parton distributions.
In a toy honeycomb-lattice model of a nucleon, gluon entanglement entropy after a sudden quark removal is dominated by dynamically generated contributions during time evolution.
Homotopy solutions to BFKL Pomeron evolution equations in nuclear DIS produce multiplicity distributions of produced gluons.
Polarized lepton beams control quantum discord and steering in hyperon-antihyperon pairs from e+e- annihilation, with discord persisting in separable states via transverse polarization.
A relative-entropy method with a minimum-relative-entropy hypothesis reproduces quark nPDF shapes from global fits and indicates that EPPS21 gluon central values align more closely with the hypothesis than nNNPDF3.0.
The reciprocal symmetry of the KNO-violating term yields the new constraint δ₃=0 at n=⟨n⟩ (untestable at present precision), fails globally at 13 TeV, and the derived entropy S=ln⟨n⟩+I₀−½∫e^{-z}f_s²dz matches ATLAS data at 10⁻³.
The generalized dipole model fits entropy and mean multiplicity data from proton-proton collisions significantly better than the standard 1D Mueller dipole model.
An approximate formula for the entropy of the negative binomial distribution is provided, with up to ~20% deviation from exact values for extreme parameters.
Including soft gluons in Monte Carlo generators for DIS aligns parton distributions with inclusive PDFs and makes entropy grow with decreasing x, indicating initial-state origin of the bulk entropy.
The linearly polarized gluon distribution enhances entanglement of heavy quark pairs in electron-nucleus collisions when total and relative transverse momenta are orthogonal.
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Emergent Local Phase-Space Scaling in Small-x Gluon Evolution
After Q_s-adaptive coarse graining, conditional gluon Husimi momentum distributions from fixed-coupling SO(3)-BK evolution collapse as functions of k/Q_s(Y,b), with conditional entropy growing at unit slope versus ⟨ln Q_s²⟩.
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Soft-Radiation-Induced Decoherence of Heavy-Quark Spin Entanglement at the Electron-Ion Collider
Subleading soft-gluon recoil rotates the heavy-quark spin-correlation plane; tracing over unresolved radiation dephases in-plane coherences while protecting the normal-axis correlation.
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Reciprocal symmetry and KNO scaling violation in proton-proton collisions
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Controlling Quantum discord and steering in Electron-Positron Annihilation Using Polarized Beams
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Higher-order local constraints from reciprocal symmetry and entanglement entropy of charged-particle multiplicity distributions in $pp$ collisions
The reciprocal symmetry of the KNO-violating term yields the new constraint δ₃=0 at n=⟨n⟩ (untestable at present precision), fails globally at 13 TeV, and the derived entropy S=ln⟨n⟩+I₀−½∫e^{-z}f_s²dz matches ATLAS data at 10⁻³.
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Entropy and mean multiplicity from dipole models in the high energy limit
The generalized dipole model fits entropy and mean multiplicity data from proton-proton collisions significantly better than the standard 1D Mueller dipole model.
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An approximate formula for the entropy of the negative binomial distribution
An approximate formula for the entropy of the negative binomial distribution is provided, with up to ~20% deviation from exact values for extreme parameters.
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Entanglement entropy, Monte Carlo event generators, and soft gluons DIScovery
Including soft gluons in Monte Carlo generators for DIS aligns parton distributions with inclusive PDFs and makes entropy grow with decreasing x, indicating initial-state origin of the bulk entropy.
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Quantum entanglement in electron-nucleus collisions: Role of the linearly polarized gluon distribution
The linearly polarized gluon distribution enhances entanglement of heavy quark pairs in electron-nucleus collisions when total and relative transverse momenta are orthogonal.