Document Type
Article
Publication Date
2016
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.
Recommended Citation
Aharonov, Y., Colombo, F., Popescu, S., Sabadini, I., Struppa, D.C., Tollaksen, J., 2016. Quantum violation of the pigeonhole principle and the nature of quantum correlations. PNAS 201522411. doi:10.1073/pnas.1522411112
Peer Reviewed
1
Copyright
National Academy of Sciences
Comments
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Proceedings of the National Academy of Sciences, volume 113, issue 3, in 2016. The The definitive, peer-reviewed version is available online at DOI: 10.1073/pnas.1522411112
The final version can also be read in PubMed Central.