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Derivation of the Lewenstein–Sanpera Decomposition via Semidefinite Programming

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Abstract

In many theoretical proposals appeared recently, semidefinite programming was considered as a way to express quantum entanglement. Using semidefinite optimization method, we prove the Lewenstein–Sanpera lemma in a simple elegant manner. Particularly, using this method we obtain Lewenstein–Sanpera decomposition for some examples such as: generic two qubit state in Wootters’s basis, Iso-concurrence state, Bell decomposable state and 2 ⊗ 3 Bell decomposable state.

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Authors and Affiliations

  1. Department of Theoretical Physics and Astrophysics, Tabriz University, Tabriz, 51664, Iran

    M. A. Jafarizadeh, M. Mirzaee & M. Rezaee

  2. Institute for Studies in Theoretical Physics and Mathematics, Tehran, 19395-1795, Iran

    M. A. Jafarizadeh, M. Mirzaee & M. Rezaee

  3. Research Institute for Fundamental Sciences, Tabriz, 51664, Iran

    M. A. Jafarizadeh

Authors
  1. M. A. Jafarizadeh
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  2. M. Mirzaee
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Correspondence to M. A. Jafarizadeh.

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Jafarizadeh, M.A., Mirzaee, M. & Rezaee, M. Derivation of the Lewenstein–Sanpera Decomposition via Semidefinite Programming. Quantum Inf Process 4, 199–218 (2005). https://doi.org/10.1007/s11128-005-5657-0

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  • DOI: https://doi.org/10.1007/s11128-005-5657-0

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