Physicists have long suspected that something important was being overlooked in our understanding of quantum systems. For decades, they've studied how particles become entangled, how information spreads through materials, and how quantum states evolve over time. But all of these investigations share a common limitation: they measure correlation, not causation.
The distinction matters profoundly. Just because two quantum particles are entangled doesn't tell you which one is actually influencing the other, or by how much. It's the quantum equivalent of noticing that ice cream sales and drowning deaths both increase in summer—they're correlated, certainly, but one doesn't cause the other.
Now, researchers have demonstrated a powerful new approach to quantifying genuine causal influence in quantum many-body systems. Their findings, published in Physical Review Letters in April 2025, reveal that causation behaves very differently from correlation—especially near the exotic points where quantum materials undergo phase transitions.
The Problem with Measuring Influence
Imagine a chain of quantum particles, each one coupled to its neighbors like dancers holding hands in a line. When you disturb one particle, effects ripple outward through the chain. Traditional measurements can show you that distant particles become correlated, but they can't tell you how much one particle is actually driving changes in another.
This gap in understanding is more than academic. Quantum computers, quantum sensors, and next-generation materials all depend on understanding how quantum systems influence each other. Yet the most commonly studied measures—entanglement entropy, correlation functions, even sophisticated tools like out-of-time-ordered correlators—can only detect that a causal connection might exist. They cannot quantify its strength.
The researchers addressed this by adapting a measure called Liang information flow to the quantum realm. Originally developed for classical systems (where it has already improved climate models and artificial intelligence), quantum Liang information flow works through a clever intervention: it measures what happens when you "freeze" a quantum particle, preventing it from evolving, then compares the resulting dynamics to normal evolution.
The difference reveals true causation. If freezing particle B changes how particle A evolves, particle B must be causally influencing particle A. The magnitude of that change quantifies the strength of the causal influence.
Causation at the Critical Point
The researchers focused their investigation on quantum phase transitions—the strange boundary points where materials transform from one phase to another at absolute zero temperature. These aren't like water freezing or boiling; they're purely quantum phenomena driven by competing interactions rather than thermal energy.
In one model system, a chain of quantum spins that can point up or down, the team studied a transition from a state where all spins point the same direction to one where quantum fluctuations destroy any collective order. This transition occurs at a precise critical point, tuned by adjusting an external magnetic field.
What they discovered was striking: causation peaks just before the critical point, not at it.
This behavior differs fundamentally from correlation measures, which typically peak at the transition itself. The causation peak appears because competing forces in the system are nearly balanced, allowing local influences to have outsized effects. It acts as an early warning signal, a herald of the impending phase transition embedded in how particles influence each other.
In the delocalized phase, far from the critical point, the researchers found a democracy of influence. Freezing any particle had roughly equal effects on all others. But approaching criticality, this equality broke down. Nearby particles began to exert disproportionate causal influence while distant effects diminished, reflecting the restriction of information flow that occurs as the system approaches a localized state.
Beyond Classical Intuition
Perhaps the most intriguing finding emerged from examining exactly how causal influence propagates through the quantum chain. In integrable systems (those solvable by exact mathematical methods), the results followed an intuitive picture where "quasiparticles" (wave-like excitations) carry influence at a maximum speed, creating a spreading envelope of causation.
But near the critical point, something stranger appeared: a subtle quantum nonlocality that exceeded this simple quasiparticle picture. The researchers traced this to the participation of special quantum states with diverging correlation lengths, extended wave patterns that span the entire system near criticality. These states exert causal influence across distances without any propagating wave, a genuinely quantum phenomenon with no classical analogue.
For non-integrable systems (those lacking exact solutions and more representative of real materials), the researchers found that causation behavior depends sensitively on the initial state. Starting from low energy states preserved the peak near criticality, but high energy initial states produced causation maxima unrelated to the phase transition. This demonstrates that maximum causation and quantum criticality are distinct phenomena, though they often coincide.
Why It Matters
The ability to measure causation, not just correlation, opens new possibilities for understanding and controlling quantum systems.
In quantum computing, identifying which qubits causally influence others most strongly could help optimize gate operations and error correction. In quantum materials, causation patterns could serve as diagnostic tools for identifying phase transitions without requiring full knowledge of the equilibrium state—useful when that state is too complex to calculate.
The researchers suggest their approach could help tackle bottlenecks in quantum annealing, a computational technique that searches for optimal solutions by steering quantum systems through phase transitions. Causation peaks naturally reveal which interactions dominate near transitions, offering guidance for improving these schedules.
Looking forward, the team proposes testing their predictions in trapped ion experiments or D-wave quantum annealers, where chains of hundreds of coupled quantum spins can already be controlled and measured. The key experimental steps involve measuring quantum states with and without freezing selected particles—technically demanding but feasible with current technology.
More broadly, this work illustrates how adapting concepts from classical information theory to quantum mechanics can yield unexpected insights. Causation, influence, and information flow are concepts that seem intuitively clear in everyday experience. But quantum mechanics forces us to rebuild them from scratch, and in doing so, reveals phenomena—like quantum nonlocal causation—that simply don't exist in the classical world.
The distinction between correlation and causation, often emphasized in statistics and science communication, turns out to matter just as much in quantum physics. And now, for the first time, we have a rigorous way to measure the difference.
Publication Details
Published online: April 18, 2025
Journal: Physical Review Letters
Publisher: American Physical Society
DOI: https://doi.org/10.1103/PhysRevLett.134.150202
Credit and Disclaimer
This article is based on original research published in Physical Review Letters by scientists from University College London and the University of Electronic Science and Technology of China. The content has been adapted for general audiences while maintaining complete scientific accuracy. Readers are strongly encouraged to consult the full research article for comprehensive technical details, complete datasets, detailed methodologies, experimental protocols, and supplementary information via the DOI link provided above. All scientific findings, data, and conclusions presented here are derived directly from the original publication, and full credit belongs to the research team and their institutions.
