Physicists have since devised more practical, experimentally implementable versions of the original Bell-Kochen-Specker theorem involving multiple entangled particles, where a particular measurement on one particle defines a “context” for the others. While the proof indicated that quantum theory demands contextuality, there was no way to actually demonstrate this through 117 simultaneous measurements of a single particle. So the physicists concluded that there is no way a particle can have fixed hidden variables that remain the same regardless of context. The outcome of a measurement could not possibly return both 0 and 1. While they had previously assigned a value of 0 to the spin along this direction, the 101 rule was now dictating that the spin must be 1.
They continued until, in the 117th direction, the contradiction cropped up. They then repeatedly rotated the direction of their hypothetical measurement and measured again, each time either freely assigning a value to the outcome or deducing what the value must be in order to satisfy the 101 rule together with directions they had previously considered. They then conducted a hypothetical spin measurement along some unique direction, assigning either 0 or 1 to the outcome. First, they assumed that each particle had a fixed, intrinsic value for each direction of spin. Kochen and Specker used this rule to arrive at a contradiction. Quantum theory says that the magnitudes of the spins along three perpendicular directions must obey the “101 rule”: The outcomes of two of the measurements must be 1 and the other must be 0. The researchers then asked: Is it possible that the particle secretly “knows” what the result of every possible measurement will be before it is measured? In other words, could they assign a fixed value - a hidden variable - to all outcomes of all possible measurements at once? Measuring the spin’s magnitude along any direction always results in one of two outcomes: 1 or 0. In Kochen and Specker’s version of the proof, they considered a single particle with a quantum property called spin, which has both a magnitude and a direction. He and, separately, Simon Kochen and Ernst Specker showed that it is impossible for a quantum system to have hidden variables that define the values of all their properties in all possible contexts. The information contained in the entangled pair must be shared nonlocally between the particles.īell also proved a similar theorem about contextuality. By comparing the outcomes of measurements of two entangled particles, he showed with his eponymous theorem of 1965 that the high degree of correlations between the particles can’t possibly be explained in terms of local “hidden variables” defining each one’s separate properties.
The Northern Irish physicist John Stewart Bell is widely credited with showing that quantum systems can be nonlocal. In February, Cabello, in collaboration with Kihwan Kim at Tsinghua University in Beijing, China, published a paper in which they claimed to have performed the first loophole-free experimental test of contextuality. Researchers have also found tantalizing links between contextuality and problems that quantum computers can efficiently solve that ordinary computers cannot investigating these links could help guide researchers in developing new quantum computing approaches and algorithms.Īnd with renewed theoretical interest comes a renewed experimental effort to prove that our world is indeed contextual. “So is more general in some sense, and I think this is important to really understand the power of quantum systems and to go deeper into why quantum theory is the way it is.” A single particle, for instance, is a quantum system “in which you cannot even think about nonlocality,” since the particle is only in one location, said Bárbara Amaral, a physicist at the University of São Paulo in Brazil. Although contextuality has lived in nonlocality’s shadow for over 50 years, quantum physicists now consider it more of a hallmark feature of quantum systems than nonlocality is.
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