An international team of physicists has used the principle of entanglement entropy to examine how particles are produced in high-energy electron–proton collisions. Led by Kong Tu at Brookhaven National Laboratory in the US, the researchers showed that quarks and gluons in protons are deeply entangled and approach a state of maximum entanglement when they take part in high-energy collisions.

While particle physicists have made significant progress in understanding the inner structures of protons, neutrons, and other hadrons, there is still much to learn. Quantum chromodynamics (QCD) says that the proton and other hadrons comprise quarks, which are tightly bound together via exchanges of gluons – mediators of the strong force. However, using QCD to calculate the properties of hadrons is notoriously difficult except under certain special circumstances.

Calculations can be simplified by describing the quarks and gluons as partons in a model that was developed in late 1960s by James Bjorken, Richard Feynman, Vladimir Gribov and others. “Here, all the partons within a proton appear ‘frozen’ when the proton is moving very fast relative to an observer, such as in high-energy particle colliders,” explains Tu.

Dynamic and deeply complex interactions

While the parton model is useful for interpreting the results of particle collisions, it cannot fully capture the dynamic and deeply complex interactions between quarks and gluons within protons and other hadrons. These interactions are quantum in nature and therefore involve entanglement. This is a purely quantum phenomenon whereby a group of particles can be more highly correlated than is possible in classical physics.

“To analyse this concept of entanglement, we utilize a tool from quantum information science named entanglement entropy, which quantifies the degree of entanglement within a system,” Tu explains.

In physics, entropy is used to quantify the degree of randomness and disorder in a system. However, it can also be used in information theory to measure the degree of uncertainty within a set of possible outcomes.

“In terms of information theory, entropy measures the minimum amount of information required to describe a system,” Tu says. “The higher the entropy, the more information is needed to describe the system, meaning there is more uncertainty in the system. This provides a dynamic picture of a complex proton structure at high energy.”

Deeply entangled

In this context, particles in a system with high entanglement entropy will be deeply entangled – whereas those in a system with low entanglement entropy will be mostly uncorrelated.

In recent studies, entanglement entropy has been used to described how hadrons are produced through deep inelastic scattering interactions – such as when an electron or neutrino collides with a hadron at high energy. However, the evolution with energy of entanglement entropy within protons had gone largely unexplored. “Before we did this work, no one had looked at entanglement inside of a proton in experimental high-energy collision data,” says Tu.

Now, Tu’s team investigated how entanglement entropy varies with the speed of the proton – and how this relationship relates to the hadrons created during inelastic collisions.

Matching experimental data

Their study revealed that the equations of QCD can accurately predict the evolution of entanglement entropy – with their results closely matching with experimental collision data. Perhaps most strikingly, they discovered that if this entanglement entropy is increased at high energies, it may approach a state of maximum entanglement under certain conditions. This high degree of entropy is evident in the large numbers of particles that are produced in electron–proton collisions.

The researchers are now confident that their approach could lead to further insights about QCD. “This method serves as a powerful tool for studying not only the structure of the proton, but also those of the nucleons within atomic nuclei.” Tu explains. “It is particularly useful for investigating the underlying mechanisms by which nucleons are modified in the nuclear environment.”

In the future, Tu and colleagues hope that their model could boost our understanding of processes such as the formation and fragmentation of hadrons within the high-energy jets created in particle collisions, and the resulting shift in parton distributions within atomic nuclei. Ultimately, this could lead to a fresh new perspective on the inner workings of QCD.

The research is described in Reports on Progress in Physics.