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Workshop on Quantum Computation, Communication, and Cryptography

TQC 2009: Theory of Quantum Computation, Communication, and Cryptography pp 94–106Cite as

On the Power of the PPT Constraint in the Symmetric Extensions Test for Separability

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5906))

Abstract

In this paper, we analyze the efficiency of entanglement criteria based on symmetric extensions and PPT symmetric extensions to solve the weak membership problem of separability WEMP(S). We observe that the set of states admitting an N-PPT symmetric extension converges to the set of all separable states quadratically faster than the set of states admitting a general N-symmetric extension. As a result, we show that the PPT constraint in the symmetric extensions criterion reduces the dominant factor on time complexity from \(\left ( k_1 /\delta \right )^{6d_B}\) to \(\left ( k_2/\delta \right )^{4d_B}\), where δ is the accuracy parameter of WMEM(S).

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Author information

Authors and Affiliations

  1. Institute for Mathematical Sciences, Imperial College London, 53 Prince’s Gate, London, SW7 2PG, UK

    Miguel Navascués, Masaki Owari & Martin B. Plenio

  2. QOLS, Blackett Laboratory, Imperial College London, London, SW7 2BW, UK

    Masaki Owari & Martin B. Plenio

  3. Institut für Theoretische Physik, Universität Ulm, D-89081, Ulm, Germany

    Martin B. Plenio

Authors
  1. Miguel Navascués
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  2. Masaki Owari
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  3. Martin B. Plenio
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Editor information

Editors and Affiliations

  1. Institute for Quantum Computing and Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, ON, Canada

    Andrew Childs

  2. Institute for Quantum Computing, University of Waterloo, N2L 3G1, Waterloo, Canada

    Michele Mosca

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© 2009 Springer-Verlag Berlin Heidelberg

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Navascués, M., Owari, M., Plenio, M.B. (2009). On the Power of the PPT Constraint in the Symmetric Extensions Test for Separability. In: Childs, A., Mosca, M. (eds) Theory of Quantum Computation, Communication, and Cryptography. TQC 2009. Lecture Notes in Computer Science, vol 5906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10698-9_10

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  • DOI: https://doi.org/10.1007/978-3-642-10698-9_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10697-2

  • Online ISBN: 978-3-642-10698-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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