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

Proceedings of the National Academy of Sciences
Aharonov, Y.Colombo, F.Popescu, S.Sabadini, I.Struppa, D.C.Tollaksen, J. School of Physics and Astronomy,
Tel Aviv University,

Schmid College of Science and Technology,
Chapman University,
Orange, CA, USA

Institute for Quantum Studies,
Chapman University,
Orange, CA, USA

Dipartimento di Matematica,
Politecnico di Milano,
Milan, Italy

H. H. Wills Physics Laboratory,
University of Bristol,
2016 Physics

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.

The article was pulished in: Proceedings of the National Academy of Sciences: 201522411.

Full article

This work was supported (in part) by the Fetzer Franklin Fund of the John E. Fetzer Memorial Trust.