Deep inelastic scattering as a probe of entanglement
Using nonlinear 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 x G ( x ) becomes very simple: S ( x ) = ln [ x G ( x ) ] . In this small x , large rapidity Y regime, all partonic microstates have equal probabilities—the proton is composed by an exponentially large number exp ( Δ Y ) of microstates that occur with equal and exponentially small probabilities exp (  Δ Y ) , where Δ is defined by x G ( x ) ~ 1 / x Δ . For this equipartitioned state, the entanglement entropy is maximal—so at small x , deep inelastic scattering probes a maximally entangled state. Here, we propose the entanglement entropy as an observable that can be studied in deep inelastic scattering. Thismore »
 Authors:

^{[1]};
^{[2]}
 Stony Brook Univ., NY (United States). Dept. of Physics and Astronomy; Brookhaven National Lab. (BNL), Upton, NY (United States). RIKEN Research Center, Dept. of Physics
 Tel Aviv Univ., Ramat Aviv (Israel). Dept. of Particle Physics; Federico Santa MarÃÂa Technical Univ. and Science and Technology Center, Valparaiso (Chile). Dept. of Physics
 Publication Date:
 Report Number(s):
 BNL1142692017JA
Journal ID: ISSN 24700010; PRVDAQ; R&D Project: KB0301020
 Grant/Contract Number:
 SC0012704; FG88ER40388; AC0298CH10886
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 95; Journal Issue: 11; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Research Org:
 Brookhaven National Laboratory (BNL), Upton, NY (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
 OSTI Identifier:
 1392245
 Alternate Identifier(s):
 OSTI ID: 1363840