Scientists uncovered universal laws of entanglement in any dimension. The results strengthen links between particle physics, quantum theory, and gravity.
A group of theoretical physicists has shown that quantum entanglement obeys universal principles in every dimension by applying thermal effective theory. Their findings were recently published in the journal Physical Review Letters, where the paper was selected as an Editors’ Suggestion.
“This study is the first example of applying thermal effective theory to quantum information. The results of this study demonstrate the usefulness of this approach, and we hope to further develop this approach to gain a deeper understanding of quantum entanglement structures,” said lead author and Kyushu University Institute for Advanced Study Associate Professor Yuya Kusuki.
Quantum entanglement and Rényi entropy
In classical physics, particles that are far apart act independently. In contrast, quantum physics shows that two particles can remain strongly correlated even at great distances, a phenomenon known as quantum entanglement. This effect is central to quantum technologies such as quantum computing and quantum communication, making its study essential for both theoretical insight and practical applications.
One of the main tools for characterizing entanglement is the Rényi entropy, which measures the complexity of quantum states and how information is distributed. It plays a key role in classifying quantum states, evaluating whether complex quantum systems can be simulated, and is also widely used in theoretical research on the black hole information loss paradox and quantum gravity.
Despite its importance, uncovering the structure of quantum entanglement remains a major challenge for both physics and quantum information science. Most investigations so far have been restricted to (1+1)-dimensional models, meaning one spatial dimension plus time. Extending this work to higher dimensions has proven much more complex.
A team led by Yuya Kusuki at the University of Tokyo’s Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU, WPI), together with Caltech Professor Hirosi Ooguri and researcher Sridip Pal, has now demonstrated that quantum entanglement exhibits universal patterns even in higher dimensions. They achieved this by adapting theoretical methods originally developed in particle physics to the study of quantum information.
Applying the thermal effective theory
The research team focused on the thermal effective theory, which has recently led to major advances in the analysis of higher-dimensional theories in particle physics. This is a theoretical framework designed to extract universal behavior from complex systems, based on the idea that observable quantities can often be characterized by only a small number of parameters.
By introducing this framework into quantum information theory, the team analyzed the behavior of Rényi entropy in higher-dimensional quantum systems. Rényi entropy is characterized by a parameter known as the replica number.
The team demonstrated that, in the regime of small replica number, the behavior of the Rényi entropy is universally governed by only a few parameters, such as the Casimir energy, a key physical quantity within the theory. Furthermore, by leveraging this result, the team clarified the behavior of the entanglement spectrum in the region where its eigenvalues are large.
They also investigated how universal behavior changes depending on the method used to evaluate the Rényi entropy. These findings hold not only in (1+1) dimensions, but in arbitrary spacetime dimensions, marking a significant step forward in the understanding of quantum entanglement structures in higher dimensions.
The next step for the researchers is to further generalize and refine this framework. This work represents the first demonstration that thermal effective theory can be effectively applied to the study of quantum entanglement structures in higher dimensions, and there remains ample room to further develop this approach. By improving the thermal effective theory with quantum information applications in mind, researchers could gain a deeper understanding of quantum entanglement structures in higher-dimensional systems.
On the applied side, the theoretical insights gained from this research may lead to improvements in numerical simulation methods for higher-dimensional quantum systems, propose new principles for classifying quantum many-body states, and contribute to a quantum-information-theoretic understanding of quantum gravity. These developments hold promise for broad and impactful future applications.
Reference: “Universality of Rényi Entropy in Conformal Field Theory” by Yuya Kusuki, Hirosi Ooguri and Sridip Pal, 5 August 2025, Physical Review Letters.
DOI: 10.1103/fsg7-bs7q
This research was supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632 and by the Walter Burke Institute for Theoretical Physics at Caltech. Hirosi Ooguri is also supported in part by the Simons Investigator Award (MP-SIP-00005259) and by JSPS Grants-in-Aid for Scientific Research 23K03379. His work was performed in part at the Kavli Institute for the Physics and Mathematics of the Universe at the University of Tokyo, which is supported by the World Premier International Research Center Initiative, MEXT, Japan, at the Kavli Institute for Theoretical Physics (KITP) at the University of California, Santa Barbara, which is supported by grant NSF PHY-2309135, and at the Aspen Center for Physics, which is supported by NSF grant PHY-1607611. Yuya Kusunoki is also supported by the INAMORI Frontier Program at Kyushu University and JSPS KAKENHI Grant Number 23K20046.
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