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We experimentally demonstrate that when three single photons transmit through two polarization channels, in a well-defined pre- and postselected ensemble, there are no two photons in the same polarization channel by weak-strength measurement, a counterintuitive quantum counting effect called the quantum pigeonhole paradox. We further show that this effect breaks down in second-order measurement. These results indicate the existence of the quantum pigeonhole paradox and its operating regime.
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http://dx.doi.org/10.1073/pnas.1815462116 | DOI Listing |
Proc Natl Acad Sci U S A
February 2025
Department of Physics and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, ON M5S 1A7, Canada.
We implement a variant of the quantum pigeonhole paradox thought experiment to study whether classical counting principles survive in the quantum domain. We observe strong measurements significantly violate the pigeonhole principle (that among three pigeons in two holes, at least one pair must be in the same hole) and the sum rule (that the number of pigeon pairs in the same hole is the sum of the number of pairs across each of the holes) in an ensemble that is pre- and postselected into particular separable states. To investigate whether measurement disturbance is a viable explanation for these counterintuitive phenomena, we employ a we employ variable-strength nonlocal measurements.
View Article and Find Full Text PDFProc Natl Acad Sci U S A
January 2019
Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, China;
We experimentally demonstrate that when three single photons transmit through two polarization channels, in a well-defined pre- and postselected ensemble, there are no two photons in the same polarization channel by weak-strength measurement, a counterintuitive quantum counting effect called the quantum pigeonhole paradox. We further show that this effect breaks down in second-order measurement. These results indicate the existence of the quantum pigeonhole paradox and its operating regime.
View Article and Find Full Text PDFEntropy (Basel)
August 2018
Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland.
The pigeonhole principle upholds the idea that by ascribing to three different particles either one of two properties, we necessarily end up in a situation when at least two of the particles have the same property. In quantum physics, this principle is violated in experiments involving postselection of the particles in appropriately-chosen states. Here, we give two explicit constructions using standard gates and measurements that illustrate this fact.
View Article and Find Full Text PDFProc Natl Acad Sci U S A
May 2016
Schmid College of Science and Technology, Chapman University, Orange, CA 92866; Institute for Quantum Studies, Chapman University, Orange, CA 92866;
Proc Natl Acad Sci U S A
January 2016
Schmid College of Science and Technology, Chapman University, Orange, CA 92866; Institute for Quantum Studies, Chapman University, Orange, CA 92866;
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.
View Article and Find Full Text PDF