We discuss quantum entanglement between fast and slow degrees of freedom, in a two dimensional (2D) large $N_c$ gauge theory with Dirac quarks, quantized on the light front. Using the 't Hooft wave functions, we construct the reduced density matrix for an interval in the momentum fraction $x$-space, and calculate its von Neumann entropy in terms of structure functions, that are measured by DIS on mesons (hadrons in general). We found that the entropy is bounded by an area law with logarithmic divergences, proportional to the rapidity of the meson. The evolution of the entanglement entropy with rapidity, is fixed by the cumulative singlet PDF, and bounded from above by a Kolmogorov-Sinai entropy of 1. At low-$x$, the entanglement exhibits an asymptotic expansion, similar to the forward meson-meson scattering amplitude in the Regge limit. The evolution of the entanglement entropy in parton-$x$ per unit rapidity, measures the meson singlet PDF. The re-summed entanglement entropy along the single meson Regge trajectory, is string-like. We suggest that its extension to multi-meson states, models DIS scattering on a large 2D $^\prime$nucleus$^\prime$. The result, is a large rate of change of the entanglement entropy with rapidity, that matches the current Bekenstein-Bremermann bound for maximum quantum information flow. This mechanism may be at the origin of the large entropy deposition and rapid thermalization, reported in current heavy ion colliders, and may extend to future electron-ion colliders.
We investigate the quantum entanglement in rapidity space of the soft gluon wave function of a quarkonium, in theories with non-trivial rapidity evolutions. We found that the rapidity evolution drastically changes the behavior of the entanglement entropy, at any given order in perturbation theory. At large $N_c$, the reduced density matrices that "resum" the leading rapidity-logs can be explicitly constructed, and shown to satisfy Balitsky-Kovchegov (BK)-like evolution equations. We study their entanglement entropy in a simplified $1+1$ toy model, and in 3D QCD. The entanglement entropy in the…
Quantum entanglement between partons in a strongly coupled quantum field theory
University of Science & Technology of China（中国科学技术大学）；Instituto Galego de Física de Altas Enerxías IGFAE, Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学加利西亚高能物理研究所）；Department of Physics, University of Turin（都灵大学物理系）；INFN, Section of Turin（意大利国家核物理研究院都灵分部）；Center for Frontiers in Nuclear Science, Stony Brook University（石溪大学核科学前沿中心）；Anhui Center for Fundamental Sciences in Theoretical Physics（安徽理论物理基础科学中心）；School of Mechanics and Physics, Anhui University of Science and Technology（安徽理工大学力学与物理学院）
Particle seismology: mechanical and gravitational properties from parton-hadron duality
Departamento de Física Atómica, Molecular y Nuclear and Instituto Carlos I de Física Teórica y Computacional（原子、分子和核物理系及卡洛斯一世理论与计算物理研究所）；The H. Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences（波兰科学院H.涅沃德尼察斯基核物理研究所）
To study quantum properties of the hadron wavefunction at small x, we derived the reduced density matrix for soft gluons in the CGC framework. We explicitly showed that the reduced density matrix is not diagonal in the particle number basis. The off-diagonal components are usually ignored in the conventional parton model. We thus defined the density matrix of ignorance by keeping only the part of the reduced density matrix which can be probed in a limited set of experimental measurements. We calculated Von Neumann entropy for both the reduced and ignorance density matrices. The entropy of igno…
Charged particle multiplicity distributions in positron-proton deep inelastic scattering at a centre-of-mass energy $\sqrt{s}=319$ GeV are measured. The data are collected with the H1 detector at HERA corresponding to an integrated luminosity of $136$ pb${}^{-1}$. Charged particle multiplicities are measured as a function of photon virtuality $Q^2$, inelasticity $y$ and pseudorapidity $η$ in the laboratory and the hadronic centre-of-mass frames. Predictions from different Monte Carlo models are compared to the data. The first and second moments of the multiplicity distributions are determined …
Analyzing the single inclusive annihilation spectrum of charged hadrons in $e^+e^-$ collisions, I confront the hadronization hypothesis of local parton-hadron duality with a systematic resummation of the dependence on the small energy fraction. This resummation is based on the reciprocity between time-like and space-like splitting processes in $4-2ε$-dimensions, which I extend to resum all the soft terms of the cross-section for inclusive jet production. Under the local-parton-hadron duality hypothesis, the resulting distribution of jets essentially determines the spectrum of hadrons as the je…
The relation between the gluon density in a hadron and entanglement entropy can shed a new light on the high energy scattering behavior of hadrons. Using the holographic light-front QCD framework the growth above the classical geometric cross section is directly related to the increase of the internal quantum entropy from the entangled parton distribution in hadrons. A rather consistent picture emerges from the scale dependence of the Pomeron from the QCD evolution of the gluon distribution function $g(x, μ)$, the rising of the integrated cross section in photoproduction of vector mesons, the …
Wave-particle duality and entanglement in neutrino oscillation
Indian Institute of Technology Bhilai（印度理工学院比莱分校）；Berhampur University（布巴内斯瓦尔大学）；Nimapara Autonomous College（尼马帕拉自治学院）；Siksha ’O’ Anusandhan（锡卡奥阿南桑丹大学）；Indian Institute of Science Education and Research Kolkata（加尔各答科学教育研究印度研究所）；Institute of Physics, Bhubaneswar（布巴内斯瓦尔物理研究所）
In this paper we show that QCD at high energies leads to the multiplicity distribution $\frac{σ_n}{σ_{ \rm in}}\,\,=\,\,\frac{1}{N}\,\Lb \frac{N\,-\,1}{N}\Rb^{n - 1}$, (where $N$ denotes the average number of particles), and to entanglement entropy $S \,=\,\ln N$, confirming that the partonic stat at high energy is maximally entangled. However, the value of $N$ depends on the kinematics of the parton cascade. In particular, for DIS$N = xG(x,Q)$ , where $xG$ is the gluon structure function, whil for hadron-hadron collisions, $N \propto Q^2_S(Y)$, where $Q_s$ denotes the saturation scale. We che…
High energy hadron interactions are commonly described by using a probabilistic parton model that ignores quantum entanglement present in the light-cone wave functions. Here we argue that since a high energy interaction samples an instant snapshot of the hadron wave function, the phases of different Fock state wave functions cannot be measured - therefore the light-cone density matrix has to be traced over these unobservable phases. Performing this trace with the corresponding $U(1)$ Haar integration measure leads to "Haar scrambling" of the density matrix, and to the emergence of entanglement…
Deep inelastic scattering (DIS) samples a part of the wave function of a hadron in the vicinity of the light cone. Lipatov constructed a spin chain which describes the amplitude of DIS in leading logarithmic approximation. Kharzeev and Levin proposed the entanglement entropy as an observable in DIS [Phys. Rev. D 95, 114008 (2017)], and suggested a relation between the entanglement entropy and parton distributions. Here we represent the DIS process as a local quench in the Lipatov's spin chain, and study the time evolution of the produced entanglement entropy. We show that the resulting entangl…
