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Analytical Optimization of Local Quantum Operation and Classical Communication

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The Impact of Applications on Mathematics

Part of the book series: Mathematics for Industry ((MFI,volume 1))

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Abstract

This manuscript treats the situation that a quantum state is prepared as an input and is manipulated by local quantum operations and classical communications (LOCC). We analytically optimize the LOCC. Optimizations with respect to LOCC frequently appear in theories of quantum communication and computation. However, this optimization problem is difficult, since we have to fix infinite number of parameters in order to identify the LOCC. In fact, there is no recipe for optimizing LOCC except for the case that the input state is a pure state, which is a special case of a quantum state. In this manuscript, we optimize the LOCC for non-pure input states. As a result, this analytical method enables us to solve a fundamental problem in the quantum communication theory. We think that our analysis will help us to make more general recipe to optimize LOCC.

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Author information

Authors and Affiliations

  1. NTT Communication Science Laboratories, 3-1, Morinosato Wakamiya, Kanagawa Prefecture, Atsugi-shi, Japan

    Go Kato

Authors
  1. Go Kato
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Corresponding author

Correspondence to Go Kato .

Editor information

Editors and Affiliations

  1. Institute for Mathematics and Industry, Kyushu University, Fukuoka, Japan

    Masato Wakayama

  2. CSIRO (Commonwealth Scientific and Industrial Research Organisation), Canberra, Aust Capital Terr, Australia

    Robert S. Anderssen

  3. School of Mathematical Sciences, Fudan University, Shanghai, China

    Jin Cheng

  4. Kyushu University, Fukuoka, Japan

    Yasuhide Fukumoto

  5. Institute of Natural and Mathematical Sciences, Massey University, Palmerston North, Auckland, New Zealand

    Robert McKibbin

  6. Institute of Mathematics, Free University of Berlin, Berlin, Germany

    Konrad Polthier

  7. Kyushu University, Fukuoka, Japan

    Tsuyoshi Takagi

  8. Department of Mathematics, National University of Singapore, Singapore, Singapur, Singapore

    Kim-Chuan Toh

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© 2014 Springer Japan

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Kato, G. (2014). Analytical Optimization of Local Quantum Operation and Classical Communication. In: Wakayama, M., et al. The Impact of Applications on Mathematics. Mathematics for Industry, vol 1. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54907-9_15

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  • DOI: https://doi.org/10.1007/978-4-431-54907-9_15

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  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-54906-2

  • Online ISBN: 978-4-431-54907-9

  • eBook Packages: EngineeringEngineering (R0)

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