# Modifications of the Page Curve from correlations within Hawking radiation

## Abstract

We investigate quantum correlations between successive steps of black hole evaporation and investigate whether they might resolve the black hole information paradox. ‘Small’ corrections in various models were shown to be unable to restore unitarity. We study a toy qubit model of evaporation that allows small quantum correlations between successive steps and reaffirm previous results. Then, we relax the ‘smallness’ condition and find a nontrivial upper and lower bound on the entanglement entropy change during the evaporation process. This gives a quantitative measure of the size of the correction needed to restore unitarity. We find that these entanglement entropy bounds lead to a significant deviation from the expected Page curve.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Florida, Gainesville, FL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)

- OSTI Identifier:
- 1558684

- Alternate Identifier(s):
- OSTI ID: 1765586

- Grant/Contract Number:
- SC0010296; SC0007890

- Resource Type:
- Published Article

- Journal Name:
- Physics Letters B

- Additional Journal Information:
- Journal Name: Physics Letters B Journal Volume: 797 Journal Issue: C; Journal ID: ISSN 0370-2693

- Publisher:
- Elsevier

- Country of Publication:
- Netherlands

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Black hole information paradox; Toy model black hole; Qubit model black hole; Quantum correlations; Small correction

### Citation Formats

```
Alvi, Mishkat Al, Majumdar, Mahbub, Matin, Md. Abdul, Rahat, Moinul Hossain, and Roy, Avik. Modifications of the Page Curve from correlations within Hawking radiation. Netherlands: N. p., 2019.
Web. doi:10.1016/j.physletb.2019.134881.
```

```
Alvi, Mishkat Al, Majumdar, Mahbub, Matin, Md. Abdul, Rahat, Moinul Hossain, & Roy, Avik. Modifications of the Page Curve from correlations within Hawking radiation. Netherlands. doi:10.1016/j.physletb.2019.134881.
```

```
Alvi, Mishkat Al, Majumdar, Mahbub, Matin, Md. Abdul, Rahat, Moinul Hossain, and Roy, Avik. Tue .
"Modifications of the Page Curve from correlations within Hawking radiation". Netherlands. doi:10.1016/j.physletb.2019.134881.
```

```
@article{osti_1558684,
```

title = {Modifications of the Page Curve from correlations within Hawking radiation},

author = {Alvi, Mishkat Al and Majumdar, Mahbub and Matin, Md. Abdul and Rahat, Moinul Hossain and Roy, Avik},

abstractNote = {We investigate quantum correlations between successive steps of black hole evaporation and investigate whether they might resolve the black hole information paradox. ‘Small’ corrections in various models were shown to be unable to restore unitarity. We study a toy qubit model of evaporation that allows small quantum correlations between successive steps and reaffirm previous results. Then, we relax the ‘smallness’ condition and find a nontrivial upper and lower bound on the entanglement entropy change during the evaporation process. This gives a quantitative measure of the size of the correction needed to restore unitarity. We find that these entanglement entropy bounds lead to a significant deviation from the expected Page curve.},

doi = {10.1016/j.physletb.2019.134881},

journal = {Physics Letters B},

number = C,

volume = 797,

place = {Netherlands},

year = {2019},

month = {10}

}

DOI: 10.1016/j.physletb.2019.134881

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Works referenced in this record:

##
Black holes and the second law

journal, August 1972

- Bekenstein, J. D.
- Lettere Al Nuovo Cimento Series 2, Vol. 4, Issue 15

##
Extraction of Rotational Energy from a Black Hole

journal, February 1971

- Penrose, R.; Floyd, R. M.
- Nature Physical Science, Vol. 229, Issue 6

##
Reversible and Irreversible Transformations in Black-Hole Physics

journal, November 1970

- Christodoulou, Demetrios
- Physical Review Letters, Vol. 25, Issue 22

##
Gravitational Radiation from Colliding Black Holes

journal, May 1971

- Hawking, S. W.
- Physical Review Letters, Vol. 26, Issue 21

##
The four laws of black hole mechanics

journal, June 1973

- Bardeen, J. M.; Carter, B.; Hawking, S. W.
- Communications in Mathematical Physics, Vol. 31, Issue 2

##
Particle creation by black holes

journal, August 1975

- Hawking, S. W.
- Communications In Mathematical Physics, Vol. 43, Issue 3

##
Hawking Radiation As Tunneling

journal, December 2000

- Parikh, Maulik K.; Wilczek, Frank
- Physical Review Letters, Vol. 85, Issue 24

##
The information paradox: a pedagogical introduction

journal, October 2009

- Mathur, Samir D.
- Classical and Quantum Gravity, Vol. 26, Issue 22

##
The information paradox and the infall problem

journal, May 2011

- Mathur, Samir D.
- Classical and Quantum Gravity, Vol. 28, Issue 12

##
Correlations in Hawking radiation and the infall problem

journal, September 2011

- Mathur, Samir D.; Plumberg, Christopher J.
- Journal of High Energy Physics, Vol. 2011, Issue 9

##
Qubit models of black hole evaporation

journal, January 2013

- Avery, Steven G.
- Journal of High Energy Physics, Vol. 2013, Issue 1

##
The black hole information problem: past, present, and future

journal, July 2017

- Marolf, Donald
- Reports on Progress in Physics, Vol. 80, Issue 9

##
Time dependence of Hawking radiation entropy

journal, September 2013

- Page, Don N.
- Journal of Cosmology and Astroparticle Physics, Vol. 2013, Issue 09

##
Breakdown of predictability in gravitational collapse

journal, November 1976

- Hawking, S. W.
- Physical Review D, Vol. 14, Issue 10

##
Quantum emission from two-dimensional black holes

journal, September 1992

- Giddings, Steven B.; Nelson, William M.
- Physical Review D, Vol. 46, Issue 6

##
Hawking radiation as tunneling through the quantum horizon

journal, September 2005

- Arzano, Michele; Medved, A. Joseph M.; Vagenas, Elias C.
- Journal of High Energy Physics, Vol. 2005, Issue 09

##
Entropy is conserved in Hawking radiation as tunneling: A revisit of the black hole information loss paradox

journal, February 2011

- Zhang, Baocheng; Cai, Qing-yu; Zhan, Ming-sheng
- Annals of Physics, Vol. 326, Issue 2

##
Proof of Page’s conjecture on the average entropy of a subsystem

journal, February 1994

- Foong, S. K.; Kanno, S.
- Physical Review Letters, Vol. 72, Issue 8

##
Average Entropy of a Quantum Subsystem

journal, July 1996

- Sen, Siddhartha
- Physical Review Letters, Vol. 77, Issue 1

##
Simple proof of Page’s conjecture on the average entropy of a subsystem

journal, November 1995

- Sánchez-Ruiz, Jorge
- Physical Review E, Vol. 52, Issue 5

##
One-Shot Decoupling and Page Curves from a Dynamical Model for Black Hole Evaporation

journal, March 2016

- Brádler, Kamil; Adami, Christoph
- Physical Review Letters, Vol. 116, Issue 10

##
Quantum information transfer and models for black hole mechanics

journal, March 2013

- Giddings, Steven B.; Shi, Yinbo
- Physical Review D, Vol. 87, Issue 6