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Nothing is stronger than quantum connections, and now we know what keeps them in check
By David Freeman -
May 11, 2025



Quantum physics is filled with baffling phenomena, but few are as consistently astonishing as quantum correlations. These connections between particles extend across space and defy the expectations of classical physics. When two particles are entangled, the measurement of one appears to instantaneously determine the state of the other, no matter the distance between them. This feature is not hypothetical. It has been confirmed in numerous experiments and has practical applications in cryptography and emerging technologies. What has remained unclear is why these correlations, as strange and powerful as they are, never go beyond a certain strength. If quantum mechanics allows for these unusual interactions, what prevents them from being even stronger? A group of researchers may have finally answered that question, using a principle grounded in logic and graph theory.

The idea revolves around what is called the exclusivity principle. This principle is not based on energy, space, or any traditional physical concept. Instead, it is based on probability and the structure of measurement scenarios. Simply put, it states that for a set of mutually exclusive events, the total probability of all of them occurring cannot exceed one. In the realm of quantum mechanics, where events are not deterministic and outcomes are distributed across probabilities, this becomes a powerful constraint.

To understand the significance of this, it helps to consider how quantum correlations differ from classical ones. In classical systems, two objects may have related properties, like two coins designed to always land the same way. But in quantum systems, the correlation is not just about shared properties. Instead, it reflects how the act of measurement on one object influences the outcomes of another in a way that cannot be mimicked by any classical system without violating fundamental assumptions about locality or realism.

Physicists have known for decades that quantum correlations are bounded. For example, in the famous case of Bell inequalities, quantum mechanics predicts that certain combinations of measurements can exceed classical limits, but only up to a specific point. Beyond that, no experimental result has ever breached the boundary predicted by quantum theory. The question has lingered as to whether that upper limit reflects some deeper physical law, or whether it is just a coincidence of the current mathematical framework.

The researchers addressed this question by focusing on the mathematical structures known as exclusivity graphs. In these graphs, each vertex represents a possible outcome of a measurement. An edge between two vertices indicates that those two outcomes are mutually exclusive — they cannot happen at the same time. The structure of the graph captures the logical constraints on how outcomes relate to one another. Using this framework, the researchers were able to map the possible probability distributions that quantum theory allows.

What they found is that the exclusivity principle, when applied within this graphical framework, tightly bounds the probabilities in a way that aligns perfectly with quantum predictions. The key lies in how these graphs behave when paired with their complementary versions. For any given exclusivity graph, the complement graph represents a set of events with a different exclusivity relationship. The researchers proved that if the quantum correlations associated with the complement graph are all permitted, then the exclusivity principle naturally rules out any correlation stronger than those allowed by quantum theory in the original graph.

One of the more striking results comes from considering self-complementary graphs. These are graphs that are, in essence, their own complements. When the exclusivity principle is applied to such graphs, it not only replicates the known quantum limits but also excludes any set of correlations that would exceed those limits. This is not a numerical coincidence. It is a rigorous consequence of the principle. In this context, the exclusivity principle alone is sufficient to prohibit any theoretical scenario that predicts stronger-than-quantum correlations.

This has major implications for how physicists interpret the nature of quantum mechanics. It suggests that the strength of quantum correlations is not arbitrary, nor is it merely a feature of current theory that might someday be overturned. Instead, it could be the result of a logical boundary built into the structure of how measurements can interact. If that is the case, then any future attempt to construct a theory that goes beyond quantum mechanics would have to either break the exclusivity principle or accept that its predictions cannot include stronger correlations.

To support their findings, the researchers also showed how the exclusivity principle behaves with vertex-transitive graphs. These are graphs where each vertex plays the same role in terms of the graph’s structure. Such graphs are often used in physics because they model symmetrical and unbiased measurement setups. The team demonstrated that for these graphs, the exclusivity principle again reproduces the exact quantum maximum. This is especially significant for well-known quantum inequalities such as the Clauser-Horne-Shimony-Holt (CHSH) inequality, which models a basic two-party entanglement scenario. The exclusivity principle not only matches the known quantum limits in these cases but also rules out the hypothetical models known as nonlocal boxes, which allow for stronger-than-quantum correlations while still preserving some aspects of causality.

These results are not purely theoretical. They offer a path for experimental verification. By designing experiments based on graphs with specific exclusivity properties, physicists can test whether nature ever exceeds the bounds predicted by the principle. So far, no such violations have been observed. In fact, all high-precision tests continue to align perfectly with quantum mechanics, further supporting the idea that the exclusivity principle is a fundamental feature of reality.

What makes this line of research particularly compelling is that it does not require any change to existing physics. There is no need to introduce new particles or unknown forces. The exclusivity principle is based on a clear and intuitive idea — that mutually exclusive events cannot all be likely at the same time. Its power comes from the way this simple idea, when combined with the mathematical structure of quantum measurements, leads to sharp and precise constraints on what is possible.

Moreover, this principle is not tied to any particular experimental setup. It applies across the board, whether the system involves photons, ions, spins, or other quantum systems. That universality suggests that the principle might be deeply embedded in the logic of nature, not just a quirk of current theory.

Previous efforts to explain the limits of quantum correlations have proposed various physical principles, such as no-signaling, information causality, or local orthogonality. While each of these provides some insight, none has the same reach as the exclusivity principle when applied to a general set of measurement scenarios. This broader applicability gives it a unique status in the growing effort to understand why quantum mechanics takes the form that it does.

One important aspect of the research is that it bridges the gap between two areas of study that are often treated separately. On one hand, quantum theory is built on Hilbert spaces, operators, and probabilistic postulates. On the other hand, graph theory deals with logical relationships and combinatorial structures. The exclusivity principle serves as a link between these domains, showing that the logical structure of measurement outcomes is not just a curiosity but may be essential to the foundations of the theory itself.

Even though this line of reasoning does not explain everything about quantum mechanics, it addresses one of the central puzzles. If quantum correlations are the strongest in nature, what sets the ceiling? The answer appears to lie not in the hardware of the universe but in the software — the logical constraints on what can be measured and how those measurements can relate.

This does not mean that the story of quantum theory is complete. But it does mean that any future developments will need to account for the exclusivity principle as a built-in limitation. Researchers looking to go beyond quantum mechanics will need to contend with the fact that the very structure of measurement may already enforce the limits they seek to surpass.

As experiments become more refined and as new technologies allow for more complex tests of quantum systems, the predictions made by the exclusivity principle will remain under scrutiny. If they continue to hold, then the principle will stand as one of the most important tools for understanding the architecture of the quantum world. It transforms the question from why quantum correlations stop where they do, to how a simple rule manages to hold together a theory as strange and successful as quantum mechanics.

For now, there is no evidence that anything stronger than quantum correlations exists. With this new work, there may finally be an explanation for why that has always been the case. It is not a limit imposed by unknown forces, but a result of what is mathematically and logically permitted within the structure of possible events. In that sense, quantum mechanics may not just be one way the world could work. It may be the only way that is logically consistent with how information and measurement behave. That insight does not just reinforce what is already known. It may be the key to understanding why quantum theory has remained unchallenged for nearly a century.

Source:

Amaral, B., Terra Cunha, M., & Cabello, A. (2013). The exclusivity principle forbids sets of correlations larger than the quantum set (arXiv:1306.6289v2). arXiv. https://arxiv.org/abs/1306.6289