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Entanglement condition for W type multimode states and schemes for experimental realization

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Abstract

We derive a class of inequality relations, using both the sum uncertainty relations of su(2) algebra operators and the Schrodinger–Robertson uncertainty relation of partially transposed su(1,1) algebra operators, to detect the three-mode entanglement of non-Gaussian states of electromagnetic field. These operators are quadratic in mode creation and annihilation operators. The inseparability condition obtained using su(2) algebra operators is shown to guarantee the violation of Schrodinger–Robertson uncertainty relation of partially transposed su(1,1) algebra operators. The obtained inseparability condition incorporates all the required bipartite entanglement conditions to detect the W type three-mode entangled states and hence it is shown to be a necessary condition for W type three-mode entangled states. A general form for a family of such inseparability conditions is provided. The results derived for three-mode systems are generalized to multimode systems. Experimental schemes using symmetric multiport beam splitters and multi-Λ EIT system are proposed to test the violation of multimode separability condition.

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Authors and Affiliations

  1. Department of Physics, Thiagarajar College, 625009, Madurai, Tamil Nadu, India

    Karthick Selvan

  2. Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, 741246, Mohanpur, West Bengal, India

    Prasanta K. Panigrahi

Authors
  1. Karthick Selvan
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  2. Prasanta K. Panigrahi
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Correspondence to Karthick Selvan or Prasanta K. Panigrahi.

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Selvan, K., Panigrahi, P.K. Entanglement condition for W type multimode states and schemes for experimental realization. Eur. Phys. J. D 73, 127 (2019). https://doi.org/10.1140/epjd/e2019-100012-7

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  • DOI: https://doi.org/10.1140/epjd/e2019-100012-7

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