Three-way quantum correlations fade exponentially with distance at any temperature, study shows

February 6, 2026 Three-way quantum correlations fade exponentially with distance at any temperature, study shows by RIKEN edited by Lisa Lock, reviewed by Robert Egan Lisa Lock scientific editor Meet our editorial team Behind our editorial process Robert Egan associate editor Meet our editorial team Behind our editorial process Editors' notes This article has been reviewed according to Science X's editorial process and policies. Editors have highlighted the following attributes while ensuring the content's credibility: fact-checked peer-reviewed publication trusted source proofread The GIST Add as preferred source Quasilocality of the effective interaction terms. Credit: Physical Review X (2025). DOI: 10.1103/9hx7-pzxw The properties of a quantum material are driven by links between its electrons known as quantum correlations. A RIKEN researcher has shown mathematically that, at non-zero temperatures, these connections can only exist over very short distances when more than two particles are involved. This finding, now published in Physical Review X, sets a fundamental limit on just how "exotic" a quantum material can be under realistic, finite-temperature conditions. A fascinating aspect of quantum physics is the concept that two particles that are spatially separated can communicate with each other. This so-called "spooky action at a distance," as Einstein referred to it, is crucial for understanding the origin of the exotic properties that arise in some materials, particularly at low temperatures. These unusual material properties are determined by the exact nature of the quantum correlation, and the material is said to be in a specific quantum phase. This is analogous to the traditional phases of matter—solid, liquid, and gas—being defined by the chemical interactions between the atoms. Many quantum phases can be explained by considering correlations between just two particles. Recently, however, even more strange phases have been identified which can only be described by evoking connections between more than two particles. These correlations are less well understood than those between two particles. For example, it was unclear how far a correlation between more than two particles could exist. Previous studies had only analyzed three-party correlations in special models and parameter regimes; for example, at high temperature or with strong simplifying assumptions. Now, Tomotaka Kuwahara of the RIKEN Center for Quantum Computing has rigorously proved that genuinely three-way quantum correlations cannot stretch over long distances in any thermal equilibrium state at any temperature. The first step was to define a measure of correlation strength. Kuwahara used a metric called conditional mutual information. "I showed mathematically that the conditional mutual information between distant regions always decays exponentially with the distance between them," explains Kuwahara. Kuwahara proved that thermal quantum systems must obey a quantum analog of the Hammersley–Clifford rule, which states that if we know everything about a middle region, then the distant two regions are essentially independent, and genuinely three-way correlations cannot extend far. Kuwahara next hopes to go beyond the thermal equilibrium case considered in this work. "A natural step is to build a similar universal theory of quantum entanglement for more general steady states, including systems that are driven or carry currents and are not exactly in equilibrium, and to tackle the much harder zero-temperature regime," he says. Publication details Tomotaka Kuwahara, Clustering of Conditional Mutual Information and Quantum Markov Structure at Arbitrary Temperatures, Physical Review X (2025). DOI: 10.1103/9hx7-pzxw Journal information: Physical Review X Key concepts Quantum correlations, foundations & formalismQuantum statistical mechanicsThermal propertiesQuantum many-body systems Provided by RIKEN Citation: Three-way quantum correlations fade exponentially with distance at any temperature, study shows (2026, February 6) retrieved 9 February 2026 from https://phys.org/news/2026-02-quantum-exponentially-distance-temperature.html This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. The content is provided for information purposes only. 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