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Wehrl entropy of entangled oscillators from the Segal–Bargmann formalism

  • Regular Article – Quantum Optics
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Abstract

In this manuscript, we study the Wehrl entropy of entangled oscillators. This semiclassical entropy associated with the phase-space description of quantum mechanics can be used for formulating uncertainty relations and for a quantification of entanglement. We focus on a system of two coupled oscillators described within its Segal–Bargmann space. This Hilbert space of holomorphic functions integrable with respect to a given Gaussian-like measure is particularly convenient to deal with harmonic oscillators. Indeed, the Stone–von Neumann theorem allows us to work in this space in a full correspondence with the ladder operators formalism. In addition, the Husimi pseudoprobability distribution is directly computed within the Segal–Bargmann formalism. Once we obtain the Husimi function, we analyse the Wehrl entropy and mutual information.

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This manuscript has no associated data or the data will not be deposited. Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.

Notes

  1. This expression holds as long as each term is finite. Clearly, this is our case for finite coupling \(\eta \).

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Acknowledgements

We are grateful to Ángel Rivas for useful discussions. This work was partially supported by the MICINN (Ministerio de Ciencia e Innovación, Spain) project PID2019-107394GB-I00/AEI/10.13039/501100011033 (AEI/FEDER, UE). This article/publication is based upon work from COST Action COSMIC WISPers CA21106, supported by COST (European Cooperation in Science and Technology). JARC acknowledges support by Institut Pascal at Université Paris-Saclay during the Paris-Saclay Astroparticle Symposium 2022, with the support of the P2IO Laboratory of Excellence (program “Investissements d’avenir” ANR-11-IDEX-0003-01 Paris-Saclay and ANR-10-LABX-0038), the P2I axis of the Graduate School of Physics of Université Paris-Saclay, as well as IJCLab, CEA, APPEC, IAS, OSUPS, and the IN2P3 master project UCMN.

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Authors and Affiliations

  1. Departamento de Física Teórica, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, Plaza de Ciencias 1, 28040, Madrid, Spain

    David Alonso-López, Jose A. R. Cembranos, David Díaz-Guerra & Andrés Mínguez-Sánchez

  2. Institute of Particle and Cosmos Physics (IPARCOS), Facultad de Ciencias Físicas, Universidad Complutense de Madrid, Plaza de Ciencias 1, 28040, Madrid, Spain

    Jose A. R. Cembranos

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  1. David Alonso-López
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  2. Jose A. R. Cembranos
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  3. David Díaz-Guerra
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  4. Andrés Mínguez-Sánchez
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All authors contributed equally to this manuscript.

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Correspondence to David Díaz-Guerra.

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Alonso-López, D., Cembranos, J.A.R., Díaz-Guerra, D. et al. Wehrl entropy of entangled oscillators from the Segal–Bargmann formalism. Eur. Phys. J. D 77, 43 (2023). https://doi.org/10.1140/epjd/s10053-023-00629-1

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