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arXiv:2002.06990 · Physical Review Research

Footprints of quantum pigeons

Gregory Reznik, Shrobona Bagchi, Justin Dressel, Lev Vaidman

Published Apr 3, 2020• 9 citations
arXivHTMLPDF

Abstract

This paper proposes a quantum setup violating the pigeonhole principle. It describes how the counterfactual reasoning of the paradox may be operationally grounded in the analysis of the tiny footprints left in the environment by the pigeons. Identifying the drawbacks of recent experiments of the quantum pigeonhole effect, the authors argue that a definitive experimental violation of the pigeonhole principle is still needed and propose an implementation using modern quantum computing hardware.

DOI
10.1103/physrevresearch.2.023004

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This paper proposes a quantum setup violating the pigeonhole principle. It describes how the counterfactual reasoning of the paradox may be operationally grounded in the analysis of the tiny footprints left in the environment by the pigeons. Identifying the drawbacks of recent experiments of the quantum pigeonhole effect, the authors argue that a definitive experimental violation of the pigeonhole principle is still needed and propose an implementation using modern quantum computing hardware.
The findings in the paper 'The quantum pigeonhole principle and the nature of quantum correlations', (arXiv 1407.3194), by Aharonov, Colombo, Popescu, Sabadini, Struppa and Tollaksen are scrutinized. I argue that some of the conclusions in the paper are ambiguous in the sense that they depend on the precise way one defines correlations, and that the 'first experiments' the authors suggest has little if any bearing on their main theses. The far-reaching conclusions the authors reach seems, therefore, premature.
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.
Quantum pigeonhole principle states that if there are three pigeons and two boxes then there are instances where no two pigeons are in the same box which seems to defy classical pigeonhole counting principle. Here, we investigate the quantum pigeonhole effect on the ibmqx2 superconducting chip with five physical qubits. We also observe the same effect in a proposed non-local circuit which avoid any direct physical interactions between the qubits which may lead to some unknown local effects. We use the standard quantum gate operations and measurement to construct the required quantum circuits on IBM quantum experience platform. We perform the experiment and simulation which illustrates the fact that no two qubits (pigeons) are in the same quantum state (boxes). The experimental results obtained using IBM quantum computer are in good agreement with theoretical predictions.
Quantum pigeonhole principle states that if there are three pigeons and two boxes then there are instances where no two pigeons are in the same box which seems to defy classical pigeonhole counting principle. Here, we investigate the quantum pigeonhole effect on the ibmqx2 superconducting chip with five physical qubits. We also observe the same effect in a proposed non-local circuit which avoid any direct physical interactions between the qubits which may lead to some unknown local effects. We use the standard quantum gate operations and measurement to construct the required quantum circuits on IBM quantum experience platform. We perform the experiment and simulation which illustrates the fact that no two qubits (pigeons) are in the same quantum state (boxes). The experimental results obtained using IBM quantum computer are in good agreement with theoretical predictions.