On the power of the PPT constraint in the symmetric extensions test for separability

  • Authors:

  • Miguel Navascués;Masaki Owari;Martin B. Plenio

  • Affiliations:

  • Institute for Mathematical Sciences, Imperial College London, London, UK;Institute for Mathematical Sciences, Imperial College London, London, UK;Institute for Mathematical Sciences, Imperial College London, London, UK

  • Venue:
  • TQC'09 Proceedings of the 4th international conference on Theory of Quantum Computation, Communication, and Cryptography
  • Year:
  • 2009

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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).