Deep inelastic scattering as a probe of entanglement

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 $x\le 10^{-3}$; this kinematic region will be amenable to studies at the Electron Ion Collider.

13 pages, 4 figures; extended final version to appear in Physical Review D

References in corpus (5)

• The Color Glass Condensate
• Multi-particle Production and Thermalization in High-Energy QCD
• Description of F2 and FL at small x using a collinearly-improved BFKL resummation
• Dynamical entropy of dense QCD states
• Decoherence and Entropy Production in Relativistic Nuclear Collisions

Cited by in corpus (116)

• Quantum Simulation for High Energy Physics
• Entanglement and quantum tomography with top quarks at the LHC
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• Entanglement Suppression and Emergent Symmetries of Strong Interactions
• Quantum Simulating Nature's Fundamental Fields
• Quantum information with top quarks in QCD
• The EPR paradox and quantum entanglement at sub-nucleonic scales
• Entanglement Rearrangement in Self-Consistent Nuclear Structure Calculations
• Maximal Entanglement in High Energy Physics
• Deeply inelastic scattering structure functions on a hybrid quantum computer
• Thermal radiation and entanglement in proton-proton collisions at the LHC
• Diffractive Dijet Production and Wigner Distributions from the Color Glass Condensate
• Dynamics of entanglement in expanding quantum fields
• Thermal excitation spectrum from entanglement in an expanding quantum string
• Single-particle digitization strategy for quantum computation of a ${\varphi }^4$ scalar field theory
• The Present and Future of QCD
• Scattering of mesons in quantum simulators
• The Color Glass Condensate density matrix: Lindblad evolution, entanglement entropy and Wigner functional
• Deep inelastic scattering as a probe of entanglement: confronting experimental data
• Thermalization of Gauge Theories from their Entanglement Spectrum
• High-Energy Collision of Quarks and Mesons in the Schwinger Model: From Tensor Networks to Circuit QED
• Evaluation of Entanglement Entropy in High Energy Elastic Scattering
• Tree-level entanglement in Quantum Electrodynamics
• Classical and quantum entropy of parton distributions
• Entanglement entropy, entropy production and time evolution in high energy QCD
• Thermal behavior and entanglement in Pb-Pb and p-p collisions
• Maximally entangled proton and charged hadron multiplicity in Deep Inelastic Scattering
• Evidence for the maximally entangled low $x$ proton in Deep Inelastic Scattering from H1 data
• Systematically Localizable Operators for Quantum Simulations of Quantum Field Theories
• The Entropy of a Jet
• Investigating entanglement entropy at small-x in DIS off protons and nuclei
• Entanglement, partial set of measurements, and diagonality of the density matrix in the parton model
• Quantum information approach to high energy interactions
• Entanglement entropy production in deep inelastic scattering
• Confinement and Kink Entanglement Asymmetry on a Quantum Ising Chain
• High energy QCD: multiplicity distribution and entanglement entropy
• QCD evolution of entanglement entropy
• Thermodynamics from relative entropy
• Quantum tomography for collider physics: Illustrations with lepton pair production
• Entanglement in Reggeized Scattering using AdS/CFT
• Geometric Quantum Information Structure in Quantum Fields and their Lattice Simulation
• Entanglement Spheres and a UV-IR connection in Effective Field Theories
• Chiral symmetry breaking, entanglement, and the nucleon spin decomposition
• Liouvillian Dynamics of the Open Schwinger Model: String Breaking and Kinetic Dissipation in a Thermal Medium
• Rapidity evolution of the entanglement entropy in quarkonium: parton and string duality
• Second law of thermodynamics for relativistic fluids formulated with relative entropy
• Quantum simulation of entanglement and hadronization in jet production: lessons from the massive Schwinger model
• Quark and gluon entanglement in the proton on the light cone at intermediate $x$
• Novel observables for exploring QCD collective evolution and quantum entanglement within individual jets
• Universality of minimal length
• Quantum Simulations of SO(5) Many-Fermion Systems using Qudits
• Gibbs entropy from entanglement in electric quenches
• Entanglement in a holographic Schwinger pair with confinement
• Analysis of multiplicity dependencies of midrapidity pt distributions of identified charged particles in p+p collisions at (s)1/2=7 TeV at the LHC
• Hadronic structure on the light-front V. Diquarks, Nucleons and multiquark Fock components
• Quantum Entanglement and Thermal Behavior in Charged-Current Weak Interactions
• Investigating the QCD dynamical entropy in high-energy hadronic collisions
• High energy QCD: multiplicity dependence of quarkonia production
• Entanglement in massive Schwinger model at finite temperature and density
• Page Entropy of Proton System in Deep-Inelastic-Scattering at Small-$x$
• Entanglement entropy of the proton in coordinate space
• Thermal and hard scales in transverse momentum distributions, fluctuations and entanglement
• Light-front wave functions of mesons, baryons and pentaquarks, with topology-induced local 4-quark interaction
• Entanglement entropy and flow in two dimensional QCD: parton and string duality
• Gluon Quasi Particles and the CGC Density Matrix
• Thermal radiation and inclusive production in the KLN model for ion-ion collisions
• Entanglement as a probe of hadronization
• Thermal radiation and inclusive production in the CGC/saturation approach at high energies
• Lectures on nonperturbative QCD ( Nonperturbative Topological Phenomena in QCD and Related Theories)
• Nuclei in the toy world: beyond the Pomeron in zero transverse dimensions
• Soft and hard scales of the transverse momentum distribution in the Color String Percolation Model
• Entanglement Structures in Quantum Field Theories II: Distortions of Vacuum Correlations Through the Lens of Local Observers
• Spatial entanglement in two dimensional QCD: Renyi and Ryu-Takayanagi entropies
• Multiplicity distribution of dipoles in QCD from Le, Mueller and Munier equation
• Quark pair angular correlations in the proton: entropy versus entanglement negativity
• Gluon Shadowing and Nuclear Entanglement
• Characterizing Proton-Proton Collisions at the Large Hadron Collider with Thermal Properties
• Quantum Entanglement and the Thermal Hadron
• Entropy from entangled parton states and high-energy scattering behavior
• Determination of the entanglement entropy in elastic scattering using model-independent method for hadron femtoscopy
• The effect of the fluctuating proton size on the study of chiral magnetic effect in proton-nucleus collisions
• Bethe Ansatz for XXX chain with negative spin
• 1+1D Hadrons Minimize their Biparton Renyi Free Energy
• Universal rapidity scaling of entanglement entropy inside hadrons from conformal invariance
• Thermal freeze-out parameters and pseudo-entropy from charged hadron spectra in high energy collisions
• Quantum entanglement correlations in double quark PDFs
• Entanglement features in scattering mediated by heavy particles
• Information scrambling and entanglement in quantum approximate optimization algorithm circuits
• Classicalization and unitarization of wee partons in QCD and Gravity: The CGC-Black Hole correspondence
• Probing Quantum Phenomena through Photoproduction in Relativistic Heavy-Ion Collisions
• Geometric Poisson distribution of photons produced in the ultrarelativistic hadronic collisions
• Entanglement entropy, Monte Carlo event generators, and soft gluons DIScovery
• Why does the thermal model for hadron production in heavy ion collisions work?
• Relaxation and correlation times of nonequilibrium multiparticle systems
• Entanglement Negativity of Spin-Orbit Correlations in a general Qubit-Qudit Setup
• The 3D entangled structure of the proton; transverse degrees of freedom in QCD, momenta, spins and more
• Partial-transpose-guided entanglement classes and minimum noise filtering in many-body Gaussian quantum systems
• Entropy and multiplicity of hadrons in the high energy limit within dipole cascade models
• Thermal nature of confining strings
• Entanglement, Complexity, and Causal Asymmetry in Quantum Theories
• Classical information entropy of parton distribution functions and an application in searching gluon saturation
• Identification of a natural fieldlike entanglement resource in trapped-ion chains
• The "DIS and Related Subjects" Strategy Document: Fundamental Science from Lepton-Hadron Scattering
• A Monte Carlo study of multiplicity fluctuations in proton-proton collisions at $\sqrt{s}=$~7~TeV
• Maximal Entanglement: Applications in Quantum Information and Particle Physics
• Quantum entanglement between partons in a strongly coupled quantum field theory
• Yangian symmetry applied to Quantum chromodynamics
• Chirality distributions inside baryons in $\mathrm{QC}{\mathrm{D}}_2$
• Small $x$ behavior in QCD from maximal entanglement and conformal invariance
• The energy dependence of the multiplicity moments at the LHC
• Evolution of entropy at small $x$
• Thermal behavior, entanglement entropy and parton distributions
• Emergent symmetries of the Standard Model
• HERA data on azimuthal decorrelation and charged particle multiplicity spectra probing QCD dynamics and quantum entanglement effects
• Entanglement, Trace Anomaly and Confinement in QCD
• Genuine tripartite entanglement in Bhabha scattering with an entangled spectator particle