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Quantum violation of the pigeonhole principle and the nature of quantum correlations

  1. Jeff Tollaksenb,c
  1. aSchool of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel;
  2. bSchmid College of Science and Technology, Chapman University, Orange, CA 92866;
  3. cInstitute for Quantum Studies, Chapman University, Orange, CA 92866;
  4. dDipartimento di Matematica, Politecnico di Milano, 20133 Milan, Italy;
  5. eH. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
  1. Contributed by Yakir Aharonov, November 12, 2015 (sent for review April 3, 2015; reviewed by Charles H. Bennett and Lucien Hardy)

Significance

We show that quantum mechanics violates one of the fundamental principles of nature: If you put three particles in two boxes, necessarily two particles will end up in the same box. We find instances when three quantum particles are put in two boxes, yet no two particles are in the same box, a seemingly impossible and absurd effect. This is only one of a host of related quantum effects which we discovered and which point to a very interesting structure of quantum mechanics that was hitherto unnoticed and has major implications for our understanding of nature. It requires us to revisit some of the most basic notions of quantum physics––the notions of separability, of correlations, and of interactions.

Abstract

The pigeonhole principle: “If you put three pigeons in two pigeonholes, at least two of the pigeons end up in the same hole,” is an obvious yet fundamental principle of nature as it captures the very essence of counting. Here however we show that in quantum mechanics this is not true! We find instances when three quantum particles are put in two boxes, yet no two particles are in the same box. Furthermore, we show that the above “quantum pigeonhole principle” is only one of a host of related quantum effects, and points to a very interesting structure of quantum mechanics that was hitherto unnoticed. Our results shed new light on the very notions of separability and correlations in quantum mechanics and on the nature of interactions. It also presents a new role for entanglement, complementary to the usual one. Finally, interferometric experiments that illustrate our effects are proposed.

Footnotes

  • ?1To whom correspondence should be addressed. Email: aharonov{at}chapman.edu.

Freely available online through the PNAS open access option.

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