The strange connections between quantum objects are the strongest relationships physicists can detect 鈥� and the mathematics of graphs may help explain why that is.
鈥淲e are touching the question of, in some way, why quantum theory is as it is,鈥� says at聽the State University of Campinas in Brazil. Together with and , also at the State University of Campinas, he has now offered one mathematically compelling answer to that question.
Quantum objects can be connected, or correlated, so strongly that measuring the properties of one can reveal those of another 鈥� even when the objects are incredibly far apart. The most famous example of this phenomenon is quantum entanglement, but there is really a whole set of ways in which quantum objects can be correlated. Classical objects can also be correlated 鈥� they can have properties that are related 鈥� but the connection between the objects is never as strong as in the quantum realm.
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Although quantum correlations sound mysterious, they operate within set limits. For example, when the connection between objects becomes weak enough, the correlation crosses the line from quantum into classical behaviour. And though the connection between quantum objects can also be much stronger, even that strength reaches a maximum value. In other words, quantum correlations can differ from classical ones only so much.
The researchers wanted to understand whether there is a physical law or principle that could explain why these deviations can鈥檛 get larger. Even more tantalisingly, answering this question would explain why correlations stronger than quantum ones have never been recorded in the lab, says Nogueira.
He and his colleagues found that answer in the exclusivity principle, an idea that explores how to measure the properties of a collection of quantum objects. The exclusivity principle shows that, if it isn鈥檛 possible to simultaneously measure the properties of a pair of quantum objects within that larger collection, then it will also be impossible to measure those same properties of the whole collection all at once.
The team combined this principle with the mathematics of 鈥渆xclusive graphs鈥�, which show the relationships between different measurements of a set of quantum objects. Analysing the similarities between many such graphs ultimately led them to a rigorous proof showing that the exclusivity principle can explain why quantum correlations behave the way they do.
鈥淚f the statistical聽observations predicted by quantum mechanics are all realised 鈥� and聽assuming one additional physical axiom, the exclusivity principle 鈥撀爐hen all statistical observations occurring in nature are explained聽by quantum mechanics,鈥� says at the Autonomous University of Barcelona in Spain. The finding builds on work聽from 2014, which Winter says was a breakthrough.
鈥淭his is really a brutal result,鈥� says at the University of Seville in Spain, who was part of the 2014 research team along with Terra Cunha. 鈥淨uantum mechanics produces a very specific, detailed set of signatures. If you find a way to reproduce that, you are touching the bones of the theory, you are understanding how nature works to produce that.鈥�
He says there are further mathematical arguments showing that the exclusivity principle may be a feature of any realistic theory of how we make measurements. If so, that would make quantum theory in some sense inevitable 鈥� and the exclusivity principle itself a physical law.
Cabello and his colleagues have done some preliminary experiments related to the exclusivity principle in the past, but he says that future experiments may make this approach to explaining quantum theory more mainstream. Terra Cunha says he feels similarly 鈥� experiments such as those with quantum light are bound to push his team鈥檚 work towards an even deeper understanding of quantum theory.
Journal reference:
Physical Review A,
