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Photons reveal a weird effect called the quantum pigeonhole paradox

Three quantum ‘birds’ can fit in two ‘pigeonholes’ without any two being in the same hole

6:00am, February 13, 2019
two pigeons, each sitting in a cubbyhole

STRANGE BIRDS  Two pigeons can sit comfortably in two holes, but add a third bird and they’ll have to share. But three quantum particles can occupy two states without any having the same state, scientists have shown.

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Quantum pigeons don’t like to share.

In keeping with a mathematical concept known as the pigeonhole principle, roosting pigeons have to cram together if there are more pigeons than spots available, with some birds sharing holes. But photons, or quantum particles of light, can violate that rule, according to an experiment reported in the Jan. 29 Proceedings of the National Academy of Sciences.

The pigeonhole principle states that, if three pigeons are roosting in two holes, one hole must contain at least two birds. Though seemingly obvious, the idea helps define the fundamentals of what numbers are and what it means to count things. But in the quantum realm, scientists had predicted that three “pigeons” — technically, quantum particles — could squeeze into two holes without any one particle sharing a hole with another, in what’s known as the quantum pigeonhole effect (SN Online: 7/18/14).

The “quantum pigeonhole effect challenges our basic understanding…. So a clear experimental verification is highly needed,” study coauthors Chao-Yang Lu and Jian-Wei Pan, physicists at the University of Science and Technology of China in Hefei, wrote in an e-mail. “The quantum pigeonhole may have potential applications to find more complex and fundamental quantum effects.”

In the study, three photons took the place of the pigeons. Rather than crowding the photons into holes, the researchers studied the polarization of the particles, or the orientation of the photons’ wiggling electromagnetic waves, which can be either horizontal or vertical. Since there were three photons and two polarizations, standard math would suggest that at least two must have had the same polarization. When the scientists compared the particles’ polarizations, the team found that no two particles matched, verifying that the quantum pigeonhole effect is real.

The mind-bending behavior is the result of a combination of already strange quantum effects. The photons begin the experiment in an odd kind of limbo called a superposition, meaning they are polarized both horizontally and vertically at the same time. When two photons’ polarizations are compared, the measurement induces ethereal links between the particles, known as quantum entanglement. These counterintuitive properties allow the particles to do unthinkable things.

While the result isn’t the first experimental confirmation of the idea, it improves on previous efforts. “I believe this paper is the best experiment done so far,” says Jeff Tollaksen of Chapman University in Orange, Calif., who was part of a team of theoretical physicists that originally proposed the effect in 2014.

The study is the first to confirm that quantum pigeons misbehave only under a specific condition. Tollaksen and his colleagues had predicted that, in order for the effect to occur, the measurement of the polarizations must be gentle, so as not to perturb the delicate quantum particles. The new work confirmed that the measurement has to be weak for the effect to occur.

Quantum mechanics is known for its odd animal-themed paradoxes — typically involving cats. Schrödinger’s cat is the star of a famous conundrum in which a feline appears to be simultaneously alive and dead (SN: 6/25/16, p. 9). And quantum “Cheshire cats” appear when particles are separated from their properties, similar to how the Alice in Wonderland cat’s grin separated from its face (SN: 9/6/14, p. 12). Like the rest of the quantum menagerie, the quantum pigeonhole effect “shows something extremely surprising, if not at first blush seemingly impossible,” Tollaksen says.


M.-C. Chen et al. Experimental demonstration of quantum pigeonhole paradox. Proceedings of the National Academy of Sciences. Vol 116, January 29, 2019, p. 1549. doi:10.1073/pnas.1815462116.

Further Reading

E. Conover. Schrödinger’s cat now dead and alive in two boxes at once. Science News. Vol. 189, June 25, 2016, p. 9.

A. Grant. Light mimics hotel with limitless vacancies. Science News. Vol. 188, November 28, 2015, p. 11.

A. Grant. Quantum Cheshire Cat experiment splits particles from their properties. Science News. Vol. 186, September 6, 2014, p. 12.

T. Siegfried. You shouldn’t try to pigeonhole quantum physics. Science News Online, July 18, 2014.

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