# A creepy quantum phenomenon you may not have heard of – contextuality

##### Katie McCormick

PhD in quantum physics, freelance journalist for Quanta Magazine

In their proof that the world is contextual, the scientists created a network of possible particle spin values measured in different directions. There is an opinion that in the future these experiments can be used to study the possibilities of quantum computing devices. Details before the start of our __flagship course in Data Science__.

Perhaps the most remarkable oddity of quantum mechanics is nonlocality. Measure one particle in an entangled pair, and this measurement, as if tearing apart a considerable space between the particles, will instantly affect the second particle; “spooky action at a distance” – as Albert Einstein called this phenomenon – became the main object of research in quantum theory.

“Nonlocality is exciting. It is like magic,” says a physicist from the University of Seville in Spain. Adan Cabello.

But Cabello and his colleagues are interested in an equally impressive but little-studied side of quantum mechanics: its contextuality. It implies the existence of particle properties such as position or polarization only in the context of measurement. Here, particle properties are not fixed numbers, but rather “words” whose meanings can change depending on the context. Compare: Time flies *like* an arrow (“Time flies *how* arrow”) and Fruit flies *like* bananas (“Fruit flies *love* bananas).

For more than half a century, contextuality has been in the shadow of nonlocality, but today quantum physicists believe that contextuality is more important than nonlocality in quantum systems. According to Barbara Amaral, a physicist at the University of São Paulo in Brazil, a single particle is a quantum system “in which you can’t even think of nonlocality” because the particle is in only one place. “So it (contextuality) is in a sense more general. I think this is important for a real understanding of the power of quantum systems and quantum theory as it is,” says B. Amaral.

The scientists also found an interesting relationship between contextuality and tasks that can be efficiently solved on quantum computers but not on ordinary computers. Its study can help in the development of new approaches and algorithms for quantum computing.

The interest of theorists was followed by a new attempt to experimentally prove the contextuality of the world. In February, Cabello, together with Kihwang Kim of Tsinghua University in Beijing, published workwhere they wrote about their first pilot study of flawless contextuality.

### 117th direction

Proof The nonlocality of quantum systems is attributed to the Northern Irish physicist John Stuart Bell. By comparing the results of measurements of two entangled particles, using the theorem he published in 1965, which now bears his name, Bell proved that the high degree of correlation between particles cannot be explained by local “hidden variables” that determine the individual properties of each of these particles. The information contained in an entangled pair must be shared nonlocally between particles.

John Bell, Simon Kochen and Ernst Specker proved the theorem in the late 1960s. They showed that quantum systems might not have fixed values for all properties in all contexts.

## Photos of scientists, from top to bottom in order in the text

*CERN PhotoLab, courtesy of Simon Kochen, Wilhelm Pleyer of the ETH Library Collection*

Bell proved and a similar contextuality theorem. He and in parallel Simon Kochen with Ernst Specker showedthat in a quantum system there cannot be hidden variables, with the help of which the values of all their properties are determined in all possible contexts.

Kochen and Specker’s version of the proof considered a single particle, a spin with a quantum property that has magnitude and direction. When the magnitude of the spin is measured in any direction, one of two results is always obtained: 1 or 0. The scientists asked the question: “Is it possible that the particle secretly “knows” the result of any measurement before the measurements”? In other words, is it possible to assign a fixed value – a latent variable – to all the results of all possible measurements at once?

According to quantum theory, the magnitudes of spins in three perpendicular directions must comply with the “rule of 101”: the results of two measurements must be equal to 1, and the third – 0. Kochen and Specker used this rule and came up with a contradiction. They first assumed that each particle has a fixed, intrinsic value for each spin direction. Then they made a hypothetical measurement of the spin in a direction different from the others, and assigned the result 0 or 1 – and re-shifted the direction of the hypothetical measurement, took the measurement again, each time either arbitrarily assigning a value to the result, or fitting it to rule 101 along with the directions already considered.

A contradiction arose in the 117th direction: previously, the spin in this direction was assigned the value 0, and now, according to the rule 101, it should be 1. As a result, measurements cannot return both 0 and 1. Therefore, physicists came to the conclusion that a particle cannot have fixed hidden variables, unchanged in any context.

Although the proof pointed out that quantum theory needed contextuality, it was impossible to demonstrate this in 117 simultaneous measurements of a single particle. Since then, physicists have formulated more practical, experimentally implementable versions of the original Bell, Kochen, and Specker theorem (with several entangled particles), where a particular dimension of one particle determines the “context” for other dimensions.

### Question after question

In 2009, contextuality—it seems to be an esoteric aspect of the inner fabric of reality—had a direct application: scientists proved that one of the simplified versions of Bell, Cochen, and Specker’s original theorem is equivalent to basic quantum computing.

Named “Mermin’s star” after its author David Mermin, the proof looked at different combinations of contextual measurements that could be performed on three entangled qubits. The logic of the formation of subsequent results by previous measurements has become the basis for quantum computing based on measurements. This discovery meant that contextuality was probably the key to understanding the reason why quantum computers can solve certain problems faster than classical ones. This is a question over which scientists have struggled with all their might.

University of British Columbia physicist and pioneer of measurement-based quantum computing Robert Raussendorf proved that in order for a quantum computer to surpass a classical one in some tasks, contextuality is necessary. But Raussendorf believes that it is not only about her. Does contextuality help quantum computers here? This is a question, he says, “probably not quite the right one.” “But we need to move from question to question: we ask a question with an understanding of how to ask; We get an answer and ask the next one.

### Research without flaws

Some scholars have pointed to flaws in Bell, Cochen, and Specker’s conclusion about the contextuality of the world. They argue that context-independent latent variables are not excluded reliably.

In February, Cabello and Kim announced that they had eliminated all possible flaws, running the Bell, Cochen, and Specker experiment “without flaws.”

This experiment involved measuring the spins of two entangled trapped ions in different directions, where the choice of measuring one ion determined the context for the other. Physicists have shown that although the measurement of one ion occurs without physical influence on the other, the context and, consequently, the result of the measurement of the second ion change.

Skeptics will ask: “How can you be sure that the result of the second measurement is changed by the context created during the first measurement, and not by other conditions that may vary from experiment to experiment?” Cabello and Kim eliminated this “certainty flaw” by running thousands of measurements and showing that if the context doesn’t change, the results don’t change. After eliminating this and other flaws, they concluded that the only reasonable explanation for their results is contextuality.

Cabello and colleagues believe that in the future these experiments can be used to study the level of contextuality, and hence the power of quantum computing devices.

“To truly understand how the world works, you need to thoroughly understand quantum contextuality,” says Cabello.

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