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Title: Entanglement, partial set of measurements, and diagonality of the density matrix in the parton model

Abstract

We define the “entropy of ignorance” which quantifies the entropy associated with ability to perform only a partial set of measurement on a quantum system. For the parton model the entropy of ignorance is equal to the Boltzmann entropy of a classical system of partons. We analyze a calculable model used for describing low x gluons in Color Glass Condensate approach, which has similarities with the parton model of QCD. In this model we calculate the entropy of ignorance in the particle number basis as well as the entanglement entropy of the observable degrees of freedom. We find that the two are similar at high momenta, but differ by a factor of order unity at low momenta. This holds for the Renyi as well as von Neumann entropies. We conclude that the entanglement does not seem to play an important role in the context of the parton model.

Authors:
; ; ; ORCiD logo
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States); North Carolina State Univ., Raleigh, NC (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); USDOE Office of Science (SC), Nuclear Physics (NP)
OSTI Identifier:
1601068
Alternate Identifier(s):
OSTI ID: 1614692; OSTI ID: 1777932
Report Number(s):
BNL-213831-2020-JAAM
Journal ID: ISSN 2470-0010; PRVDAQ; 036017
Grant/Contract Number:  
SC0012704; SC0020081; 1913890
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 3; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; deep inelastic scattering; entanglement entropy; quantum chromodynamics

Citation Formats

Duan, Haowu, Akkaya, Candost, Kovner, Alex, and Skokov, Vladimir V. Entanglement, partial set of measurements, and diagonality of the density matrix in the parton model. United States: N. p., 2020. Web. doi:10.1103/PhysRevD.101.036017.
Duan, Haowu, Akkaya, Candost, Kovner, Alex, & Skokov, Vladimir V. Entanglement, partial set of measurements, and diagonality of the density matrix in the parton model. United States. doi:https://doi.org/10.1103/PhysRevD.101.036017
Duan, Haowu, Akkaya, Candost, Kovner, Alex, and Skokov, Vladimir V. Thu . "Entanglement, partial set of measurements, and diagonality of the density matrix in the parton model". United States. doi:https://doi.org/10.1103/PhysRevD.101.036017.
@article{osti_1601068,
title = {Entanglement, partial set of measurements, and diagonality of the density matrix in the parton model},
author = {Duan, Haowu and Akkaya, Candost and Kovner, Alex and Skokov, Vladimir V.},
abstractNote = {We define the “entropy of ignorance” which quantifies the entropy associated with ability to perform only a partial set of measurement on a quantum system. For the parton model the entropy of ignorance is equal to the Boltzmann entropy of a classical system of partons. We analyze a calculable model used for describing low x gluons in Color Glass Condensate approach, which has similarities with the parton model of QCD. In this model we calculate the entropy of ignorance in the particle number basis as well as the entanglement entropy of the observable degrees of freedom. We find that the two are similar at high momenta, but differ by a factor of order unity at low momenta. This holds for the Renyi as well as von Neumann entropies. We conclude that the entanglement does not seem to play an important role in the context of the parton model.},
doi = {10.1103/PhysRevD.101.036017},
journal = {Physical Review D},
number = 3,
volume = 101,
place = {United States},
year = {2020},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: https://doi.org/10.1103/PhysRevD.101.036017

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Cited by: 2 works
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