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

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 instan...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 2016-01, Vol.113 (3), p.532-535
Main Authors: Aharonov, Yakir, Colombo, Fabrizio, Popescu, Sandu, Sabadini, Irene, Struppa, Daniele C., Tollaksen, Jeff
Format: Article
Language:English
Subjects:
Correlation analysis
Experiments
Interferometry
Physical Sciences
Quantum physics
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Summary: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.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.1522411112