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 involved¹.

This finding 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 can 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.

Related contents

• It takes three to tangle: long-range quantum entanglement needs three-way interaction
• Extending the applicability of a key quantum law
• Tightening the math behind a key quantum process

Rate this article

Stars

Thank you!

Submit

Reference

• 1. Kuwahara, T. Clustering of conditional mutual information and quantum Markov structure at arbitrary temperatures. Physical Review X 15 041010 (2025). doi: 10.1103/9hx7-pzxw