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Entropic entanglement criteria for Fermion systems

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Abstract

Entanglement criteria for general (pure or mixed) states of systems consisting of two identical fermions are introduced. These criteria are based on appropriate inequalities involving the entropy of the global density matrix describing the total system, on the one hand, and the entropy of the one-particle reduced density matrix, on the other hand. A majorization-related relation between these two density matrices is obtained, leading to a family of entanglement criteria based on Rényi’s entropic measure. These criteria are applied to various illustrative examples of parametrized families of mixed states. The dependence of the entanglement detection efficiency on Rényi’s entropic parameter is investigated. The extension of these criteria to systems of N identical fermions is also considered.

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Authors and Affiliations

  1. Physics Department, University of Pretoria, Pretoria, 0002, South Africa

    C. Zander

  2. Instituto Carlos I de Física Teórica y Computacional and Departamento de Fisica Atomica, Molecular y Nuclear, University of Granada, Granada, Spain

    A. R. Plastino

  3. UNLP-CREG-IFILP-CONICET, National University La Plata, C.C. 727, 1900, La Plata, Argentina

    A. R. Plastino & A. Plastino

  4. Departament de Física, Universitat de les Illes Balears and IFISC-CSIC, 07122, Palma de Mallorca, Spain

    M. Casas

Authors
  1. C. Zander
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  2. A. R. Plastino
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  3. M. Casas
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  4. A. Plastino
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Corresponding author

Correspondence to A. R. Plastino.

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Zander, C., Plastino, A.R., Casas, M. et al. Entropic entanglement criteria for Fermion systems. Eur. Phys. J. D 66, 14 (2012). https://doi.org/10.1140/epjd/e2011-10654-x

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  • DOI: https://doi.org/10.1140/epjd/e2011-10654-x

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