{"title":"Maximally entangled gluons for any x","authors":"Yoshitaka Hatta, Jake Montgomery","doi":"10.1103/physrevd.111.014024","DOIUrl":null,"url":null,"abstract":"Individual quarks and gluons at small x</a:mi></a:math> inside an unpolarized hadron can be regarded as Bell states in which qubits in the spin and orbital angular momentum spaces are maximally entangled. Using the machinery of quantum information science, we generalize this observation to all values <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><c:mn>0</c:mn><c:mo><</c:mo><c:mi>x</c:mi><c:mo><</c:mo><c:mn>1</c:mn></c:math> and describe gluons (but not quarks) as maximally entangled states between a qubit and a qudit. We introduce the conditional probability distribution <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><e:mi>P</e:mi><e:mo stretchy=\"false\">(</e:mo><e:msup><e:mi>l</e:mi><e:mi>z</e:mi></e:msup><e:mo stretchy=\"false\">|</e:mo><e:msup><e:mi>s</e:mi><e:mi>z</e:mi></e:msup><e:mo stretchy=\"false\">)</e:mo></e:math> of a gluon’s orbital angular momentum <j:math xmlns:j=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><j:msup><j:mi>l</j:mi><j:mi>z</j:mi></j:msup></j:math> given its helicity <l:math xmlns:l=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><l:msup><l:mi>s</l:mi><l:mi>z</l:mi></l:msup></l:math>. Restricting to the three states <n:math xmlns:n=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><n:msup><n:mi>l</n:mi><n:mi>z</n:mi></n:msup><n:mo>=</n:mo><n:mn>0</n:mn><n:mo>,</n:mo><n:mo>±</n:mo><n:mn>1</n:mn></n:math>, which constitute a qutrit, we explicitly compute <p:math xmlns:p=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><p:mi>P</p:mi></p:math> as a function of <r:math xmlns:r=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><r:mi>x</r:mi></r:math>. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"59 1","pages":""},"PeriodicalIF":5.0000,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review D","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevd.111.014024","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
Abstract
Individual quarks and gluons at small x inside an unpolarized hadron can be regarded as Bell states in which qubits in the spin and orbital angular momentum spaces are maximally entangled. Using the machinery of quantum information science, we generalize this observation to all values 0<x<1 and describe gluons (but not quarks) as maximally entangled states between a qubit and a qudit. We introduce the conditional probability distribution P(lz|sz) of a gluon’s orbital angular momentum lz given its helicity sz. Restricting to the three states lz=0,±1, which constitute a qutrit, we explicitly compute P as a function of x. Published by the American Physical Society2025
期刊介绍:
Physical Review D (PRD) is a leading journal in elementary particle physics, field theory, gravitation, and cosmology and is one of the top-cited journals in high-energy physics.
PRD covers experimental and theoretical results in all aspects of particle physics, field theory, gravitation and cosmology, including:
Particle physics experiments,
Electroweak interactions,
Strong interactions,
Lattice field theories, lattice QCD,
Beyond the standard model physics,
Phenomenological aspects of field theory, general methods,
Gravity, cosmology, cosmic rays,
Astrophysics and astroparticle physics,
General relativity,
Formal aspects of field theory, field theory in curved space,
String theory, quantum gravity, gauge/gravity duality.