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On the Separability Criterion of Bipartite States with Certain Non-Hermitian Operators

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Abstract

We construct a density matrix whose elements are written in terms of expectation values of non-Hermitian operators and their products for arbitrary dimensional bipartite states. We then show that any expression which involves matrix elements can be reformulated by the expectation values of these non-Hermitian operators and vice versa. We consider the condition of pure states and pure product states and rewrite them in terms of expectation values and density matrix elements respectively. We utilize expectation values of these operators to present the condition for separability of C d⊗C d bipartite states. With the help of our separability criterion we detect entanglement in certain classes of higher dimensional bipartite states.

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Authors and Affiliations

  1. Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli - 620024, Tamilnadu, India

    N. Ananth & M. Senthilvelan

  2. Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA University, Thanjavur - 613401, Tamilnadu, India

    V. K. Chandrasekar

Authors
  1. N. Ananth
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  2. V. K. Chandrasekar
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  3. M. Senthilvelan
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Correspondence to M. Senthilvelan.

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Ananth, N., Chandrasekar, V.K. & Senthilvelan, M. On the Separability Criterion of Bipartite States with Certain Non-Hermitian Operators. Int J Theor Phys 54, 2632–2643 (2015). https://doi.org/10.1007/s10773-014-2495-9

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  • DOI: https://doi.org/10.1007/s10773-014-2495-9

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