# 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:

- 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}

}

DOI: https://doi.org/10.1103/PhysRevD.101.036017

*Citation information provided by*

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Works referenced in this record:

##
Thermal radiation and entanglement in proton-proton collisions at energies available at the CERN Large Hadron Collider

journal, September 2018

- Baker, O. K.; Kharzeev, D. E.
- Physical Review D, Vol. 98, Issue 5

##
Entropy of Isolated Quantum Systems after a Quench

journal, July 2011

- Santos, Lea F.; Polkovnikov, Anatoli; Rigol, Marcos
- Physical Review Letters, Vol. 107, Issue 4

##
Weak and strong typicality in quantum systems

journal, July 2012

- Santos, Lea F.; Polkovnikov, Anatoli; Rigol, Marcos
- Physical Review E, Vol. 86, Issue 1

##
From bubbles to foam: dilute to dense evolution of hadronic wave function at high energy

journal, June 2007

- Kovner, Alex; Lublinsky, Michael; Wiedemann, Urs Achim
- Journal of High Energy Physics, Vol. 2007, Issue 06

##
Entanglement entropy and entropy production in the color glass condensate framework

journal, August 2015

- Kovner, Alex; Lublinsky, Michael
- Physical Review D, Vol. 92, Issue 3

##
Gluon saturation and entropy production in proton–proton collisions

journal, November 2011

- Kutak, Krzysztof
- Physics Letters B, Vol. 705, Issue 3

##
Dynamical entropy of dense QCD states

journal, February 2013

- Peschanski, Robi
- Physical Review D, Vol. 87, Issue 3

##
General properties of entropy

journal, April 1978

- Wehrl, Alfred
- Reviews of Modern Physics, Vol. 50, Issue 2

##
Deep inelastic scattering as a probe of entanglement

journal, June 2017

- Kharzeev, Dmitri E.; Levin, Eugene M.
- Physical Review D, Vol. 95, Issue 11

##
Entanglement in Regge scattering using the AdS/CFT correspondence

journal, August 2019

- Liu, Yizhuang; Zahed, Ismail
- Physical Review D, Vol. 100, Issue 4

##
Microscopic diagonal entropy and its connection to basic thermodynamic relations

journal, February 2011

- Polkovnikov, Anatoli
- Annals of Physics, Vol. 326, Issue 2

##
Classical and quantum entropy of parton distributions

journal, May 2018

- Hagiwara, Yoshikazu; Hatta, Yoshitaka; Xiao, Bo-Wen
- Physical Review D, Vol. 97, Issue 9

##
QCD Reggeon field theory for every day: Pomeron loops included

journal, March 2009

- Altinoluk, Tolga; Kovner, Alex; Lublinsky, Michael
- Journal of High Energy Physics, Vol. 2009, Issue 03

##
The Color Glass Condensate

journal, November 2010

- Gelis, Francois; Iancu, Edmond; Jalilian-Marian, Jamal
- Annual Review of Nuclear and Particle Science, Vol. 60, Issue 1

##
Thermal behavior and entanglement in Pb-Pb and $p\text{\u2212}p$ collisions

journal, January 2019

- Feal, X.; Pajares, C.; Vazquez, R. A.
- Physical Review C, Vol. 99, Issue 1

##
Entanglement entropy of scattering particles

journal, July 2016

- Peschanski, Robi; Seki, Shigenori
- Physics Letters B, Vol. 758

##
The Color Glass Condensate density matrix: Lindblad evolution, entanglement entropy and Wigner functional

journal, May 2019

- Armesto, Néstor; Domínguez, Fabio; Kovner, Alex
- Journal of High Energy Physics, Vol. 2019, Issue 5

##
Gluon distribution functions for very large nuclei at small transverse momentum

journal, April 1994

- McLerran, Larry; Venugopalan, Raju
- Physical Review D, Vol. 49, Issue 7

##
Entropy of a Jet

journal, September 2019

- Neill, Duff; Waalewijn, Wouter J.
- Physical Review Letters, Vol. 123, Issue 14

##
Thermal excitation spectrum from entanglement in an expanding quantum string

journal, March 2018

- Berges, Jürgen; Floerchinger, Stefan; Venugopalan, Raju
- Physics Letters B, Vol. 778

##
Entanglement entropy, entropy production and time evolution in high energy QCD

journal, May 2019

- Kovner, Alex; Lublinsky, Michael; Serino, Mirko
- Physics Letters B, Vol. 792

##
Computing quark and gluon distribution functions for very large nuclei

journal, March 1994

- McLerran, Larry; Venugopalan, Raju
- Physical Review D, Vol. 49, Issue 5