News Release

Sino-Brazilian study proves compatibility of two fundamental principles of quantum theory

Non-locality and contextuality were born with quantum theory but followed independent paths for several decades

Peer-Reviewed Publication

Fundação de Amparo à Pesquisa do Estado de São Paulo

Quantum theory, which was formulated in the first three decades of the twentieth century, describes a wide array of phenomena at the molecular, atomic and subatomic scales. Among its many technological applications, three have become ubiquitous in daily life: laser barcode scanners, light-emitting diodes (LEDs) and the global positioning system (GPS).

Nevertheless, quantum physics is still not entirely understood, and some of the phenomena concerned appear to fly in the face of common sense or everyday empirical experience, surprising not only the average layperson but also physicists and philosophers of science. Some of the counterintuitive aspects of quantum theory are due to its probabilistic nature. It offers a set of rules for calculating the probabilities of the possible measurement outcomes of physical systems and in general cannot predict the actual result of a single measurement.

One of the challenging ideas presented by quantum physics is non-locality, an aspect of reality manifested when two or more systems are generated or interact in such a way that the quantum states of any system cannot be described independently of the quantum states of the others. Technically speaking, scientists call such systems entangled, since they are strongly correlated even at a distance and their quantum state is not defined by the quantum states of their component parts.

Another challenging idea, which seems to point in the opposite direction, is contextuality, according to which the outcome of measuring a quantum object depends on the context, meaning other compatible measurements performed at the same time.

Non-locality and contextuality were born with quantum theory but followed independent paths for several decades. In 2014, scientists conducted a study involving a particular case in which they showed that only one of them can be observed in a quantum system. This finding became known as monogamy. The authors conjectured that non-locality and contextuality were different facets of the same general behavior observed either in one way or the other.

Now, however, a study by Brazilian and Chinese researchers has shown both theoretically and experimentally that this is not so. An article on the study is published in Physical Review Letters and highlighted as an Editors’ Suggestion.

The research was led by Rafael Rabelo, last author of the article and a professor at the State University of Campinas’s Gleb Wataghin Institute of Physics (IFGW-UNICAMP) in Brazil. 

The first authors are Peng Xue and Lei Xiao of Beijing Computational Science Research Center in China.

The other co-authors, all affiliated with Brazilian institutions, are Gabriel Ruffolo and André Mazzari, also researchers at IFGW-UNICAMP; Marcelo Terra Cunha of the same university’s Institute of Mathematics, Statistics and Scientific Computing (IMECC-UNICAMP); and Tassius Temístocles of the Federal Institute of Alagoas.

“We proved that both phenomena can indeed be observed concurrently in quantum systems. The theoretical approach was developed here in Brazil and validated in a quantum optics experiment by our Chinese collaborators,” Rabelo told Agência FAPESP.

The new study shows definitively that two of the fundamental ways in which quantum physics differs from classical physics can be observed at the same time in the same system, contrary to the usual belief. “Non-locality and contextuality, therefore, are clearly not complementary manifestations of the same phenomenon,” Rabelo said.

In practical terms, non-locality is an important resource for quantum encryption, while contextuality is the basis for a specific quantum computing model, among other applications. “The possibility of having both at the same time in the same system could pave the way to the development of new quantum information processing and quantum communications protocols,” he said. 

Bell’s theorem

The idea of non-locality was a sort of answer to the objection raised by Albert Einstein (1879-1955) to the probabilistic nature of quantum physics. In a seminal article published in 1935, Einstein, Boris Podolsky (1896-1966) and Nathan Rosen (1909-1995), or EPR, questioned the completeness of quantum theory. They proposed a thought experiment known as the EPR paradox: to justify certain non-classical correlations deriving from entanglement, distant quantum systems would have to exchange information instantly, which is impossible according to the special theory of relativity. They concluded that this paradox was due to the incompleteness of quantum theory. The incompleteness, EPR argued, could be corrected by including local hidden variables that would make quantum physics as deterministic as classical physics.

“In 1964, British physicist J.S. Bell (1928-1990) revisited the EPR argument, introducing an elegant formalism that encompassed all theories of local hidden variables regardless of the particular properties each variable might have. Bell proved that none of these theories could reproduce the correlations between measurements performed on two systems predicted by quantum physics. In my view, this result, later known as Bell’s theorem, is one of the most important pillars of quantum physics. The property of having strong correlations that can’t be reproduced by any local theory is now known as Bell non-locality. Alain Aspect, John Clauser and Anton Zeilinger were awarded the 2022 Nobel Prize in Physics for observing Bell non-locality experimentally, among other achievements,” Rabelo said.

Another important result deriving from the discussion of hidden variables was presented in an article by Simon Kochen (1934-) and Ernst Specker (1920-2011), published in 1967. The authors demonstrated that, owing to the structure and mathematical properties of quantum measurements, any theory of hidden variables that reproduces the predictions of quantum physics must exhibit a contextuality aspect.

“Despite the common motivation, studies of Bell non-locality and Kochen-Specker contextuality followed independent paths for quite a long time. Only recently has there been growing interest in finding out whether both phenomena could be manifested concurrently in the same physical system. In an article published in 2014, Pawel Kurzynski, Adán Cabello and Dagomir Kaszlikowski said no. They showed why through a particular case but an interesting one, nonetheless. We’ve now refuted that ‘no’ in our study,” Rabelo said.

The study was supported by FAPESP via a Young Investigator Grant awarded to Rabelo; a doctoral scholarship awarded to Ruffolo; and a master’s scholarship awarded to Mazzari.

About São Paulo Research Foundation (FAPESP)

The São Paulo Research Foundation (FAPESP) is a public institution with the mission of supporting scientific research in all fields of knowledge by awarding scholarships, fellowships and grants to investigators linked with higher education and research institutions in the State of São Paulo, Brazil. FAPESP is aware that the very best research can only be done by working with the best researchers internationally. Therefore, it has established partnerships with funding agencies, higher education, private companies, and research organizations in other countries known for the quality of their research and has been encouraging scientists funded by its grants to further develop their international collaboration. You can learn more about FAPESP at and visit FAPESP news agency at to keep updated with the latest scientific breakthroughs FAPESP helps achieve through its many programs, awards and research centers. You may also subscribe to FAPESP news agency at


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