News Release

Pomerons in the proton do not destroy maximal entanglement

Peer-Reviewed Publication

The Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences

Collision of a photon with a pomeron inside a proton.


A photon inside a proton can collide with a temporary complex of gluons, whose color charges (here shown in red, green and blue) can be collectively neutralized.

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Credit: Source: IFJ PAN

When a high-energy photon strikes a proton, secondary particles diverge in a way that indicates that the inside of the proton is maximally entangled. An international team of physicists with the participation of the Institute of Nuclear Physics of the Polish Academy of Sciences in Cracow has just demonstrated that maximum entanglement is present in the proton even in those cases where pomerons are involved in the collisions.



Eighteen months ago, it was shown that different parts of the interior of the proton must be maximally quantum entangled with each other. This result, achieved with the participation of Prof. Krzysztof Kutak from the Institute of Nuclear Physics of the Polish Academy of Sciences (IFJ PAN) in Cracow and Prof. Martin Hentschinski from the Universidad de las Americas Puebla in Mexico, was a consequence of considerations and observations of collisions of high-energy photons with quarks and gluons in protons and supported the hypothesis presented a few years earlier by professors Dimitri Kharzeev and Eugene Levin.


Now, in a paper published in the journal Physical Review Letters, an international team of physicists has been presented a complementary analysis of entanglement for collisions between photons and protons in which secondary particles (hadrons) are produced by a process called diffractive deep inelastic scattering. The main question was: does entanglement also occur among quarks and gluons in these cases, and if so, is it also maximal?


Putting it in simple terms: physicists speak of entanglement between various quantum objects when the values of some feature of these objects are related. Quantum entanglement is not observed in the classical world, but its essence is easily explained by the toss of two coins. Each coin has two sides and, when it falls, it can take one of two mutually exclusive values (heads or tails) with the same probability. We would be dealing with the analog of quantum entanglement if, when tossing two coins simultaneously, we always obtain either only two different results (heads and tails) or two identical results (two heads or two tails). Here, entanglement would be maximal because no value would be favoured – the probability of a coin being in the state of heads or tails would still be 50%. If entanglement were not maximal, the situation would be different. We would not always observe the same two combinations, but sometimes also the other.


“In nuclear physics, the existence of a maximal entanglement state can be seen in experimental data when, looking at it, we know that... we know nothing. In certain collisions of an electron with a proton, called deep inelastic scattering, the proton breaks up completely and many particles subject to the strong interactions – so called hadrons – are being produced. We are then dealing with a maximally entangled state of the proton, whenever we cannot predict how many hadrons will be created in a given collision,”  as Prof. Kutak explains.


Earlier studies of the maximal entanglement of the proton's interior addressed the above mentioned case, where hadrons were produced in deep inelastic scattering of an electron and a proton. Such  reactions are easy to spot in experiments because they result in secondary particles diverging in virtually all  directions (i.e. those involving the primary direction of proton motion).


“It is known, however, that roughly every tenth collision occurs differently: behind the collision point, in certain angular intervals, no particles are seen at all. It is precisely such processes that we call diffraction or exclusive production, and they are at the centre of our current research into quantum entanglement,” as Prof. Kutak adds.


Production in deep inelastic process results from the interaction of a photon with partons (quarks and gluons) in a proton. In the case of diffractive production, the photon also interacts with a parton in the proton, but one that is part of a larger structure, referred to as a pomeron.


The most important quantum feature of gluons is their colour (which has nothing to do with colour as we know it in everyday life, apart from the name). Secondary particles, observed in detectors as an effect of collisions, are the result of processes in which quarks and gluons in a proton exchange their colour charge. However, gluons can form bound states called pomerons, where the colour is mutually neutralised. When, during a collision between a photon and a parton, it turns out that the parton was part of a pomeron, the collision will not produce hadrons diverging over the full angular range covered by the detectors. Instead, some of the detectors, theoretically able to see the particles produced during the collision phase in question, will remain silent.


The international team of physicists was able to show that during collisions involving pomerons, a state is also created inside the proton in which all particles are maximally entangled. However, a difference from the previously analysed cases is apparent: when pomerons are involved, the maximum entanglement appears at slightly higher energy.


The present research complements our previous knowledge of the course of events during collisions between photons and protons. Thanks to it, it can now be said that maximal entanglement is a universal phenomenon in these processes, present in both secondary particle production mechanisms known to us.


“Our result has not only theoretical, but also practical significance. Indeed, a deeper understanding of how a maximally entangled state is formed inside the proton will allow for a better interpretation of results from future particle colliders such as the Electron-Ion Collider,” concludes Prof. Kutak.


On the Polish side, the research was funded by the European STRONG-2020 project and a grant from the Polish-American Kosciuszko Foundation.



The Henryk Niewodniczański Institute of Nuclear Physics (IFJ PAN) is currently one of the largest research institutes of the Polish Academy of Sciences. A wide range of research carried out at IFJ PAN covers basic and applied studies, from particle physics and astrophysics, through hadron physics, high-, medium-, and low-energy nuclear physics, condensed matter physics (including materials engineering), to various applications of nuclear physics in interdisciplinary research, covering medical physics, dosimetry, radiation and environmental biology, environmental protection, and other related disciplines. The average yearly publication output of IFJ PAN includes over 600 scientific papers in high-impact international journals. Each year the Institute hosts about 20 international and national scientific conferences. One of the most important facilities of the Institute is the Cyclotron Centre Bronowice (CCB), which is an infrastructure unique in Central Europe, serving as a clinical and research centre in the field of medical and nuclear physics. In addition, IFJ PAN runs four accredited research and measurement laboratories. IFJ PAN is a member of the Marian Smoluchowski Kraków Research Consortium: “Matter-Energy-Future”, which in the years 2012-2017 enjoyed the status of the Leading National Research Centre (KNOW) in physics. In 2017, the European Commission granted the Institute the HR Excellence in Research award. As a result of the categorization of the Ministry of Education and Science, the Institute has been classified into the A+ category (the highest scientific category in Poland) in the field of physical sciences.





Prof. Krzysztof Kutak

Institute of Nuclear Physics, Polish Academy of Sciences

tel.: +48 12 6628312






“Probing the onset of maximal entanglement inside the proton in diffractive DIS”

M. Hentschinski, D. E. Kharzeev, K. Kutak, Z. Tu

Physical Review Letters, 131, 241901, 2023

DOI: 10.1103/PhysRevLett.131.241901




The website of the Institute of Nuclear Physics, Polish Academy of Sciences.

Press releases of the Institute of Nuclear Physics, Polish Academy of Sciences.







A photon inside a proton can collide with a temporary complex of gluons, whose color charges (here shown in red, green and blue) can be collectively neutralized. (Source: IFJ PAN)

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