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Witness for Non-Quasi Maximally Entangled States

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Abstract

Maximally entangled states, defined as those states that have the maximal entanglement of formation under some entanglement measure, are the ideal resource for many quantum missions. In this paper, we call a convex roof of maximally entangled pure states a quasi maximally entangled state. First, we present the concept of a witness for non-quasi maximally entangled states, which is an observable that can distinguish some non-quasi maximally entangled states from quasi maximally entangled ones. Then we prove that every non-quasi maximally entangled state can be witnessed by a witness and obtain some necessary and sufficient conditions for an observable to be a witness for non-quasi maximally entangled states. Lastly, we give some classes of Hermitian operators, which can become witnesses. Especially, we compute non-quasi maximally entangled states that can be detected by a specific product operator.

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Acknowledgments

This subject was supported by the National Natural Science Foundation of China (Nos. 11371012, 11401359).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710119, China

    Tian Feng, Zhihua Guo & Huaixin Cao

Authors
  1. Tian Feng
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  2. Zhihua Guo
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  3. Huaixin Cao
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Correspondence to Zhihua Guo.

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Feng, T., Guo, Z. & Cao, H. Witness for Non-Quasi Maximally Entangled States. Int J Theor Phys 55, 5202–5215 (2016). https://doi.org/10.1007/s10773-016-3141-5

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  • DOI: https://doi.org/10.1007/s10773-016-3141-5

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