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Local Channels Preserving Maximal Entanglement or Schmidt Number

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Abstract

It is well know that entanglement is invariant under local unitary operations. In this paper we show that a local channel preserves maximal entanglement state (MES) or preserves pure states with Schmidt number r (r is an arbitrarily fixed integer) if and only if it is a local unitary operation. That is, the only local channel that leaves entanglement invariant is the local unitary operation.

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Acknowledgements

Y. Guo is supported by the China Postdoctoral Science Foundation funded project (Grant No. 2012M520603), the Natural Science Foundation of Shanxi (2013021001-1, 2012011001-2), the Research start-up fund for Doctors of Shanxi Datong University (Grant No. 2011-B-01) and the Natural Science Foundation of China (Grant Nos. 11171249, 11101250). Z. Bai and S. Du are supported by the Natural Science Foundation of China (Grants No. 11001230) and the Natural Science Foundation of Fujian (2013J01011).

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Authors and Affiliations

  1. Department of Mathematics, Shanxi Datong University, Datong, 037009, China

    Yu Guo

  2. Institute of Optoelectronic Engineering, Taiyuan University of Technology, Taiyuan, 030024, China

    Yu Guo

  3. School of Mathematical Sciences, Xiamen University, Xiamen, 361000, China

    Zhaofang Bai & Shuanping Du

Authors
  1. Yu Guo
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  2. Zhaofang Bai
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  3. Shuanping Du
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Correspondence to Zhaofang Bai.

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Guo, Y., Bai, Z. & Du, S. Local Channels Preserving Maximal Entanglement or Schmidt Number. Int J Theor Phys 52, 3820–3829 (2013). https://doi.org/10.1007/s10773-013-1688-y

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  • DOI: https://doi.org/10.1007/s10773-013-1688-y

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