title: Quantum violation of the pigeonhole principle and the nature of quantum correlations.
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.
authors.affiliation: School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel; Schmid College of Science and Technology, Chapman University, Orange, CA 92866; Institute for Quantum Studies, Chapman University, Orange, CA 92866; aharonov@chapman.edu.
authors.forename: Yakir
authors.initials: Y
authors.lastname: Aharonov
authors.affiliation: Dipartimento di Matematica, Politecnico di Milano, 20133 Milan, Italy;
authors.forename: Fabrizio
authors.initials: F
authors.lastname: Colombo
authors.affiliation: Institute for Quantum Studies, Chapman University, Orange, CA 92866; H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom.
authors.forename: Sandu
authors.initials: S
authors.lastname: Popescu
authors.affiliation: Dipartimento di Matematica, Politecnico di Milano, 20133 Milan, Italy;
authors.forename: Irene
authors.initials: I
authors.lastname: Sabadini
authors.affiliation: Schmid College of Science and Technology, Chapman University, Orange, CA 92866; Institute for Quantum Studies, Chapman University, Orange, CA 92866;
authors.forename: Daniele C
authors.initials: DC
authors.lastname: Struppa
authors.affiliation: Schmid College of Science and Technology, Chapman University, Orange, CA 92866; Institute for Quantum Studies, Chapman University, Orange, CA 92866;
authors.forename: Jeff
authors.initials: J
authors.lastname: Tollaksen
keywords: correlations; entanglement and quantum nonlocality; foundations of quantum mechanics; two-state vector formalism; weak value and weak measurement