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Proceedings of the National Academy of Sciences

Even quantum pigeons may thrive together

B. E. Y. Svensson

Published May 20, 2016• 5 citations
Publisher

Abstract

In a recent issue of PNAS, Aharonov et al. (1) present interesting results on correlations between three particles (“pigeons”), 1, 2 and 3, each having access to two quantum states (“boxes” and “pigeonholes”) | L > and | R >. For a preselected three-particle state |in > = | + >1 | + >2 | + >3, where | + >1 = (| L >1 + | R >1)/√2, etc. for the other particles, and for the postselected state | f > = | + i >1 | + i …

DOI
10.1073/pnas.1601890113

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In a recent issue of PNAS, Aharonov et al. (1) present interesting results on correlations between three particles (“pigeons”), 1, 2 and 3, each having access to two quantum states (“boxes” and “pigeonholes”) | L > and | R >. For a preselected three-particle state |in > = | + >1 | + >2 | + >3, where | + >1 = (| L >1 + | R >1)/√2, etc. for the other particles, and for the postselected state | f > = | + i >1 | + i …
It was recently argued that the pigeonhole principle, which states that if three pigeons are put into two pigeonholes then at least one pigeonhole must contain more than one pigeon, is violated in quantum systems [Y. Aharonov et al., PNAS 113, 532 (2016)]. An experimental verification of this effect was recently reported [M.-C. Chen et al., PNAS 116, 1549 (2019)]. In another recent experimental work, it was argued that two entities were observed to exchange properties without meeting each other [Z.-H. Liu et al., Nat. Commun. 11, 3006 (2020)]. Here we describe all these proposals and experiments as simple quantum interference effects, where no such dramatic conclusions appear. Besides demystifying some of the conclusions of the cited works, we also present physical insights for some interesting behaviors present in these treatments. For instance, we associate the anomalous particles behaviors in the quantum pigeonhole effect to a quantum interference of force.
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 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.