• Photonics Research
  • Vol. 9, Issue 7, 1379 (2021)
Pratyusha Chowdhury1、4, Arun Kumar Pati2、5, and Jing-Ling Chen3、*
Author Affiliations
  • 1Indian Institute of Technology Guwahati, Guwahati, Assam 781039, India
  • 2Quantum Information and Computation Group, Harish-Chandra Research Institute, Jhunsi, Allahabad 211019, India
  • 3Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, China
  • 4e-mail: pchowdhury@iitg.ac.in
  • 5e-mail: akpati@hri.res.in
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    DOI: 10.1364/PRJ.425101 Cite this Article Set citation alerts
    Pratyusha Chowdhury, Arun Kumar Pati, Jing-Ling Chen. Wave and particle properties can be spatially separated in a quantum entity[J]. Photonics Research, 2021, 9(7): 1379 Copy Citation Text show less

    Abstract

    Wave and particle are two fundamental properties of nature. The wave–particle duality has indicated that a quantum object may exhibit the behaviors of both wave and particle, depending upon the circumstances of the experiment. The major significance of wave–particle duality has led to a fundamental equation in quantum mechanics: the Schrödinger equation. At present, the principle of wave–particle duality has been deeply rooted in people’s hearts. This leads to a common-sense perception that wave property and particle property coexist simultaneously in a quantum entity, and these two physical attributes cannot be completely separated from each other. In classical physics, a similar common-sense thought is that a physical system is inseparable from its physical properties. However, this has been recently challenged and beaten by a quantum phenomenon called the “quantum Cheshire cat,” in which a cat and its grin can be spatially separated. In this work, we propose a thought experiment based on the technology similar to the quantum Cheshire cat. We find that wave and particle attributes of a quantum entity can be completely separated, thus successfully dismantling the wave–particle duality for a quantum entity. Our result is still consistent with the complementarity principle and deepens the understanding of quantum foundations.
    |W|Wave=eiϕ12(cosϕ12|1isinϕ12|3),|P|Particle=12(|2+eiϕ2|4).

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    |Ψi=12(|L+|R)(cosα|W+sinα|P),

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    |Ψf=12(|L|W+|R|P).

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    σ1234=[0100100000010010].

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    |R|PBS|Reiϕ12(cosϕ12|2isinϕ12|4)σ1234|Reiϕ12(cosϕ12|1isinϕ12|3)|R|W.

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    |Ψf=12(|L|W+|R|P)BS,σ1234|Ψf1=12(|L+|R)|W.

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    ΠPR=ΠRΠP=|RR||PP|,ΠPL=ΠLΠP=|LL||PP|,

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    ΠWR=ΠRΠW=|RR||WW|,ΠWL=ΠLΠW=|LL||WW|,

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    A^w=Ψf|A^|ΨiΨf|Ψi,

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    ΠPLw=0,ΠPRw=sinαcosα+sinα,ΠWRw=0,ΠWLw=cosαcosα+sinα.

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    ΠWLw+ΠPLw+ΠP¯Lw+ΠW¯Lw+ΠWRw+ΠW¯Rw+ΠPRw+ΠP¯Rw=1.

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    ΠPLw=ΠP¯Lw=ΠWRw=ΠW¯Rw=0,ΠPRw=sinαcosα+sinα,ΠP¯Rw=0,ΠWLw=cosαcosα+sinα,ΠW¯Lw=0.

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    ΠPRw+ΠWLw=1.

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    Pratyusha Chowdhury, Arun Kumar Pati, Jing-Ling Chen. Wave and particle properties can be spatially separated in a quantum entity[J]. Photonics Research, 2021, 9(7): 1379
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