On the reduction criterion for random quantum states

  title={On the reduction criterion for random quantum states},
  author={Maria A. Jivulescu and Nicolae Lupa and Ion Nechita},
  journal={Journal of Mathematical Physics},
  • Maria A. Jivulescu, Nicolae Lupa, Ion Nechita
  • Published 2014
  • Physics, Mathematics
  • Journal of Mathematical Physics
  • In this paper, we study the reduction criterion for detecting entanglement of large dimensional bipartite quantum systems. We first obtain an explicit formula for the moments of a random quantum state to which the reduction criterion has been applied. We show that the empirical eigenvalue distribution of this random matrix converges strongly to a limit that we compute, in three different asymptotic regimes. We then employ tools from free probability theory to study the asymptotic positivity of… CONTINUE READING

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