Spooky action’ at a very short distance: Scientists

map out quantum entanglement in protons

by Karen McNulty Walsh and Peter Genzer

Data from past proton-electron collisions provide strong

evidence of entanglement among the proton’s sea of

quarks (spheres) and gluons (squiggles), which may play

Type to enter textan important role in their strong-force interactions. Credit:

Valerie Lentz/Brookhaven National Laboratory

Scientists at the U.S. Department

of Energy’s (DOE) Brookhaven

National Laboratory and

collaborators have a new way to

use data from high-energy particle

smashups to peer inside protons.

Their approach uses quantum

information science to map out

how particle tracks streaming from

electron-proton collisions are

influenced by quantum

entanglement inside the proton.

The results reveal that quarks and

gluons, the fundamental building

blocks that make up a proton’sstructure, are subject to so-called

quantum entanglement. This

quirky phenomenon, famously

described by Albert Einstein as

“spooky action at a distance,”

holds that particles can know one

another’s state—for example, their

spin direction—even when they

are separated by a great distance.

In this case, entanglement occurs

over incredibly short distances—

less than one quadrillionth of a

meter inside individual protons—

and the sharing of information

extends over the entire group of

quarks and gluons in that proton.The team’s latest paper, just

published in Reports on Progress

in Physics, summarizes the

group’s six-year research effort. It

maps out precisely how

entanglement affects the

distribution of stable particles that

emerge at various angles from the

particle smashups after quarks and

gluons liberated in the collisions

coalesce to form these new

composite particles.

This new view of entanglement

among quarks and gluons adds a

layer of complexity to an evolving

picture of protons’ inner structure.

It may also offer insight into otherareas of science where

entanglement plays a role.

“Before we did this work, no one

had looked at entanglement inside

of a proton in experimental high-

energy collision data,” said

physicist Zhoudunming (Kong) Tu,

a co-author on the paper and

collaborator on this exploration

since joining Brookhaven Lab in

2018.

“For decades, we’ve had a

traditional view of the proton as a

collection of quarks and gluons

and we’ve been focused on

understanding so-called single-particle properties, including how

quarks and gluons are distributed

inside the proton.

“Now, with evidence that quarks

and gluons are entangled, this

picture has changed. We have a

much more complicated, dynamic

system,” he said. “This latest

paper refines our understanding of

how entanglement impacts proton

structure.”

Mapping out the entanglement

among quarks and gluons inside

protons could offer insight into

other complex questions in nuclear

physics, including how being partof a larger nucleus affects proton

properties.

This will be one focus of future

experiments at the Electron-Ion

Collider (EIC), a nuclear physics

research facility expected to open

at Brookhaven Lab in the 2030s.

The tools these scientists are

developing will enable predictions

for EIC experiments.

Deciphering messiness as a sign of

entanglement

For this study, the scientists used

the language and equations of

quantum information science to

predict how entanglement shouldimpact particles streaming from

electron-proton collisions. Such

collisions are a common approach

for probing proton structure, most

recently at the Hadron-Electron

Ring Accelerator (HERA) particle

collider in Hamburg, Germany,

from 1992 to 2007, and are

planned for future EIC

experiments.

This approach, published in 2017,

was developed by Dmitri

Kharzeev, a theorist affiliated with

both Brookhaven Lab and Stony

Brook University who is a co-

author on the paper, and Eugene

Levin of Tel Aviv University. Theequations predict that if the quarks

and gluons are entangled, that can

be revealed from the collision’s

entropy, or disorder.

“Think of a kid’s messy bedroom,

with laundry and other things all

over the place. In that disorganized

room, the entropy is very high,” Tu

said, contrasting it with the low-

entropy situation of his extremely

neat garage, where every tool is in

its place.

According to the calculations,

protons with maximally entangled

quarks and gluons—a high degree

of “entanglement entropy”—shouldproduce a lot of particles with a

“messy” distribution—a high

degree of entropy.

“For a maximally entangled state

of quarks and gluons, there is a

simple relation that allows us to

predict the entropy of particles

produced in a high energy

collision,” Kharzeev said. “In our

paper, we tested this relation using

experimental data.”

The scientists started by analyzing

data from proton-proton collisions

at Europe’s Large Hadron Collider,

but they also wanted to look at the

“cleaner” data produced byelectron-proton collisions. Knowing

it would be a while before the EIC

turns on, Tu joined one of the

HERA experiment collaborations,

known as H1, which still has a

crew of retired physicists meeting

occasionally to discuss their

experiment.

Tu worked with physicist Stefan

Schmitt, the current co-

spokesperson for H1 from the

Deutsches Elektronen-Synchrotron

(DESY), for three years to mine

the old data. The pair cataloged

detailed information from data

recorded in 2006–2007, including

how particle production anddistributions varied and a wide

range of other information about

the collisions that produced these

distributions. They published all

the data for others to use.

When the physicists compared the

HERA data with the entropy

calculations, the results matched

the predictions perfectly. These

analyses, including the latest

ROPP results on how particle

distributions change at various

angles from the collision point,

provide strong evidence that

quarks and gluons inside protons

are maximally entangled.The results and methods help to

lay the groundwork for future

experiments at the EIC.

Future experiments at the Electron-Ion Collider (EIC) will

reveal how being in a nucleus affects the quantum

entanglement among quarks and gluons within a proton.

Credit: Tiffany Bowman/Brookhaven National Laboratory

Statistical behavior and emergent

properties

The revelation of entanglement

among quarks and gluons shedslight on the nature of their strong-

force interactions, Kharzeev noted.

It may offer additional insight into

what keeps quarks and gluons

confined within protons, which is

one of the central questions in

nuclear physics that will be

explored at the EIC.

“Maximal entanglement inside the

proton emerges as a consequence

of strong interactions that produce

a large number of quark–antiquark

pairs and gluons,” he said.

Strong-force interactions—the

exchange of one or more gluons

among quarks—take placebetween individual particles. That

may sound just like the simplest

description of entanglement, where

two individual particles can know

about one another no matter how

far apart they are. But

entanglement, which is really an

exchange of information, is a

system-wide interaction.

“Entanglement doesn’t only

happen between two particles but

among all the particles,” Kharzeev

said.

Now that scientists have a way of

exploring this collective

entanglement, the tools ofquantum information science could

make some problems in nuclear

and particle physics easier to

understand.

“Particle collisions can be

extremely complex with many

steps that influence the outcome,”

Tu said. “But this study shows that

some outcomes, like the entropy of

the particles emerging, are

determined by the entanglement

within the protons before they

collide.

“Entropy doesn’t ‘care’ about the

complexity of all the in-between

steps. So maybe we can use this approach to explore other complex

nuclear physics phenomena

without worrying about the details

of what happens along the way.”

Thinking about the collective

behavior of a whole system rather

than individual particles is common

in other areas of physics and even

everyday life. For example, when

you think about a pot of boiling

water, you don’t really know about

the vibrational motion of each

individual water molecule. No

single water molecule can burn

you.It’s the statistical average of all the

molecules vibrating—their

collective combined behavior—that

gives rise to the property of

temperature and makes the water

feel hot. In a similar way,

understanding how one quark and

gluonbehave doesn’t immediately

convey how a proton behaves as a

whole.

“The physics perspective changes

when you have so many particles

together,” Tu said, noting that

quantum information science is a

tool to describe the statistical or

emergent behavior of the whole

system. “This approach may offerinsight into how the entanglement

of the particles leads to the group

behavior,” Tu said.

Putting the model to use

Now that the scientists have

confirmed and validated their

model, they want to use it in new

ways. For example, they want to

learn how being in a nucleus

affects the proton.

“To answer this question, we need

to collide electrons not just with

individual protons but with nuclei—

the ions of the EIC,” Tu said. “It will

be very helpful to use the same

tools to see the entanglement in aproton embedded in a nucleus—to

learn how it is impacted by the

nuclear environment.”

Will putting a proton in the very

busy nuclear environment

surrounded by lots of other

interacting protons and neutrons

wash out the individual proton’s

entanglement? Could this nuclear

environment play a role in so-

called quantum decoherence?

“Looking at entanglement in the

nuclear environment will definitely

tell us more about this quantum

behavior—how it stays coherent or

becomes decoherent—and learnmore about how it connects to the

traditional nuclear and particle

physics phenomena that we are

trying to solve,” Tu said.

“The impact of the nuclear

environment on protons and

neutrons is at the center of the EIC

science,” said Martin Hentschinski,

a co-author on the paper from the

Universidad de las Américas

Puebla (UDLAP) in Mexico.

Co-author Krzysztof Kutak of the

Polish Academy of Sciences

added, “There are many other

phenomena we want to use this

tool to study to push ourunderstanding of the structure of

visible matter to a new frontier.”

More information: Martin

Hentschinski et al, QCD evolution

of entanglement