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

Yakir Aharonov*, Fabrizio Colombo, Sandu Popescu, Irene Sabadini, Daniele C. Struppa, Jeff Tollaksen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


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.

Original languageEnglish
Pages (from-to)532-535
Number of pages4
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number3
StatePublished - 19 Jan 2016


FundersFunder number
John E. Fetzer Memorial Trust
European Research Council
Israel Science Foundation1311/14
Israeli Centers for Research Excellence


    • Correlations
    • Entanglement and quantum nonlocality
    • Foundations of quantum mechanics
    • Two-state vector formalism
    • Weak value and weak measurement


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