# 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. 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. 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}

}

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

*Citation information provided by*

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Web of Science

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